Non Linear Differential Equations Of Higher Order

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Global Behavior of Nonlinear Difference Equations of Higher Order with Applications

Author : V.L. Kocic
Publisher : Springer Science & Business Media
ISBN 13 : 9401717036
Total Pages : 237 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Global Behavior of Nonlinear Difference Equations of Higher Order with Applications by : V.L. Kocic

Download or read book Global Behavior of Nonlinear Difference Equations of Higher Order with Applications written by V.L. Kocic and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear difference equations of order greater than one are of paramount impor tance in applications where the (n + 1)st generation (or state) of the system depends on the previous k generations (or states). Such equations also appear naturally as discrete analogues and as numerical solutions of differential and delay differential equations which model various diverse phenomena in biology, ecology, physiology, physics, engineering and economics. Our aim in this monograph is to initiate a systematic study of the global behavior of solutions of nonlinear scalar difference equations of order greater than one. Our primary concern is to study the global asymptotic stability of the equilibrium solution. We are also interested in whether the solutions are bounded away from zero and infinity, in the description of the semi cycles of the solutions, and in the existence of periodic solutions. This monograph contains some recent important developments in this area together with some applications to mathematical biology. Our intention is to expose the reader to the frontiers of the subject and to formulate some important open problems that require our immediate attention.

Introduction to Nonlinear Differential and Integral Equations

Author : Harold Thayer Davis
Publisher :
ISBN 13 :
Total Pages : 590 pages
Book Rating : 4.:/5 (319 download)

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Book Synopsis Introduction to Nonlinear Differential and Integral Equations by : Harold Thayer Davis

Download or read book Introduction to Nonlinear Differential and Integral Equations written by Harold Thayer Davis and published by . This book was released on 1960 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Non-Linear Differential Equations of Higher Order

Author : R. Reissig
Publisher : Springer
ISBN 13 :
Total Pages : 696 pages
Book Rating : 4.:/5 (39 download)

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Book Synopsis Non-Linear Differential Equations of Higher Order by : R. Reissig

Download or read book Non-Linear Differential Equations of Higher Order written by R. Reissig and published by Springer. This book was released on 1974-01-31 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Differential Equations and Dynamical Systems

Author : Feliz Manuel Minhós
Publisher : MDPI
ISBN 13 : 3036507108
Total Pages : 158 pages
Book Rating : 4.0/5 (365 download)

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Book Synopsis Nonlinear Differential Equations and Dynamical Systems by : Feliz Manuel Minhós

Download or read book Nonlinear Differential Equations and Dynamical Systems written by Feliz Manuel Minhós and published by MDPI. This book was released on 2021-04-15 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Special Edition contains new results on Differential and Integral Equations and Systems, covering higher-order Initial and Boundary Value Problems, fractional differential and integral equations and applications, non-local optimal control, inverse, and higher-order nonlinear boundary value problems, distributional solutions in the form of a finite series of the Dirac delta function and its derivatives, asymptotic properties’ oscillatory theory for neutral nonlinear differential equations, the existence of extremal solutions via monotone iterative techniques, predator–prey interaction via fractional-order models, among others. Our main goal is not only to show new trends in this field but also to showcase and provide new methods and techniques that can lead to future research.

Nonlinear Ordinary Differential Equations

Author : Dominic Jordan
Publisher : Oxford University Press on Demand
ISBN 13 : 0199208247
Total Pages : 541 pages
Book Rating : 4.1/5 (992 download)

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Book Synopsis Nonlinear Ordinary Differential Equations by : Dominic Jordan

Download or read book Nonlinear Ordinary Differential Equations written by Dominic Jordan and published by Oxford University Press on Demand. This book was released on 2007-08-23 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thoroughly updated and expanded 4th edition of the classic text, including numerous worked examples, diagrams and exercises. An ideal resource for students and lecturers in engineering, mathematics and the sciences it is published alongside a separate Problems and Solutions Sourcebook containing over 500 problems and fully-worked solutions.

Nonlinear Differential Equations

Author : Svatopluk Fucik
Publisher : Elsevier
ISBN 13 : 1483278379
Total Pages : 360 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Nonlinear Differential Equations by : Svatopluk Fucik

Download or read book Nonlinear Differential Equations written by Svatopluk Fucik and published by Elsevier. This book was released on 2014-12-03 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studies in Applied Mathematics, 2: Nonlinear Differential Equations focuses on modern methods of solutions to boundary value problems in linear partial differential equations. The book first tackles linear and nonlinear equations, free boundary problem, second order equations, higher order equations, boundary conditions, and spaces of continuous functions. The text then examines the weak solution of a boundary value problem and variational and topological methods. Discussions focus on general boundary conditions for second order ordinary differential equations, minimal surfaces, existence theorems, potentials of boundary value problems, second derivative of a functional, convex functionals, Lagrange conditions, differential operators, Sobolev spaces, and boundary value problems. The manuscript examines noncoercive problems and vibrational inequalities. Topics include existence theorems, formulation of the problem, vanishing nonlinearities, jumping nonlinearities with finite jumps, rapid nonlinearities, and periodic problems. The text is highly recommended for mathematicians and engineers interested in nonlinear differential equations.

Ordinary Differential Equations

Author : J. Kurzweil
Publisher : Elsevier
ISBN 13 : 1483297659
Total Pages : 441 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Ordinary Differential Equations by : J. Kurzweil

Download or read book Ordinary Differential Equations written by J. Kurzweil and published by Elsevier. This book was released on 2014-06-28 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author, Professor Kurzweil, is one of the world's top experts in the area of ordinary differential equations - a fact fully reflected in this book. Unlike many classical texts which concentrate primarily on methods of integration of differential equations, this book pursues a modern approach: the topic is discussed in full generality which, at the same time, permits us to gain a deep insight into the theory and to develop a fruitful intuition. The basic framework of the theory is expanded by considering further important topics like stability, dependence of a solution on a parameter, Carathéodory's theory and differential relations.The book is very well written, and the prerequisites needed are minimal - some basics of analysis and linear algebra. As such, it is accessible to a wide circle of readers, in particular to non-mathematicians.

Nonlinear Differential Equations and Dynamical Systems

Author : Ferdinand Verhulst
Publisher : Springer Science & Business Media
ISBN 13 : 3642971490
Total Pages : 287 pages
Book Rating : 4.6/5 (429 download)

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Book Synopsis Nonlinear Differential Equations and Dynamical Systems by : Ferdinand Verhulst

Download or read book Nonlinear Differential Equations and Dynamical Systems written by Ferdinand Verhulst and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bridging the gap between elementary courses and the research literature in this field, the book covers the basic concepts necessary to study differential equations. Stability theory is developed, starting with linearisation methods going back to Lyapunov and Poincaré, before moving on to the global direct method. The Poincaré-Lindstedt method is introduced to approximate periodic solutions, while at the same time proving existence by the implicit function theorem. The final part covers relaxation oscillations, bifurcation theory, centre manifolds, chaos in mappings and differential equations, and Hamiltonian systems. The subject material is presented from both the qualitative and the quantitative point of view, with many examples to illustrate the theory, enabling the reader to begin research after studying this book.

Ordinary Non Linear Differential Equationsin Engineering and Physical Sciences

Author : Nw McLachlan
Publisher : Franklin Classics
ISBN 13 : 9780343267094
Total Pages : 220 pages
Book Rating : 4.2/5 (67 download)

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Book Synopsis Ordinary Non Linear Differential Equationsin Engineering and Physical Sciences by : Nw McLachlan

Download or read book Ordinary Non Linear Differential Equationsin Engineering and Physical Sciences written by Nw McLachlan and published by Franklin Classics. This book was released on 2018-10-15 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Linearization of Nonlinear Differential Equations, II

Author : Vlajko Lj Kocić
Publisher :
ISBN 13 :
Total Pages : 4 pages
Book Rating : 4.:/5 (124 download)

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Book Synopsis Linearization of Nonlinear Differential Equations, II by : Vlajko Lj Kocić

Download or read book Linearization of Nonlinear Differential Equations, II written by Vlajko Lj Kocić and published by . This book was released on 1982 with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Higher-Order Differential Equations and Elasticity

Author : Luis Manuel Braga da Costa Campos
Publisher : CRC Press
ISBN 13 : 0429644051
Total Pages : 275 pages
Book Rating : 4.4/5 (296 download)

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Book Synopsis Higher-Order Differential Equations and Elasticity by : Luis Manuel Braga da Costa Campos

Download or read book Higher-Order Differential Equations and Elasticity written by Luis Manuel Braga da Costa Campos and published by CRC Press. This book was released on 2019-11-05 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: Higher-Order Differential Equations and Elasticity is the third book within Ordinary Differential Equations with Applications to Trajectories and Vibrations, Six-volume Set. As a set, they are the fourth volume in the series Mathematics and Physics Applied to Science and Technology. This third book consists of two chapters (chapters 5 and 6 of the set). The first chapter in this book concerns non-linear differential equations of the second and higher orders. It also considers special differential equations with solutions like envelopes not included in the general integral. The methods presented include special differential equations, whose solutions include the general integral and special integrals not included in the general integral for myriad constants of integration. The methods presented include dual variables and differentials, related by Legendre transforms, that have application in thermodynamics. The second chapter concerns deformations of one (two) dimensional elastic bodies that are specified by differential equations of: (i) the second-order for non-stiff bodies like elastic strings (membranes); (ii) fourth-order for stiff bodies like bars and beams (plates). The differential equations are linear for small deformations and gradients and non-linear otherwise. The deformations for beams include bending by transverse loads and buckling by axial loads. Buckling and bending couple non-linearly for plates. The deformations depend on material properties, for example isotropic or anisotropic elastic plates, with intermediate cases such as orthotropic or pseudo-isotropic. Discusses differential equations having special integrals not contained in the general integral, like the envelope of a family of integral curves Presents differential equations of the second and higher order, including non-linear and with variable coefficients Compares relation of differentials with the principles of thermodynamics Describes deformations of non-stiff elastic bodies like strings and membranes and buckling of stiff elastic bodies like bars, beams, and plates Presents linear and non-linear waves in elastic strings, membranes, bars, beams, and plates

An Introduction to Nonlinear Partial Differential Equations

Author : J. David Logan
Publisher : John Wiley & Sons
ISBN 13 : 0470225955
Total Pages : 416 pages
Book Rating : 4.4/5 (72 download)

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Book Synopsis An Introduction to Nonlinear Partial Differential Equations by : J. David Logan

Download or read book An Introduction to Nonlinear Partial Differential Equations written by J. David Logan and published by John Wiley & Sons. This book was released on 2008-04-11 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the First Edition: "This book is well conceived and well written. The author has succeeded in producing a text on nonlinear PDEs that is not only quite readable but also accessible to students from diverse backgrounds." —SIAM Review A practical introduction to nonlinear PDEs and their real-world applications Now in a Second Edition, this popular book on nonlinear partial differential equations (PDEs) contains expanded coverage on the central topics of applied mathematics in an elementary, highly readable format and is accessible to students and researchers in the field of pure and applied mathematics. This book provides a new focus on the increasing use of mathematical applications in the life sciences, while also addressing key topics such as linear PDEs, first-order nonlinear PDEs, classical and weak solutions, shocks, hyperbolic systems, nonlinear diffusion, and elliptic equations. Unlike comparable books that typically only use formal proofs and theory to demonstrate results, An Introduction to Nonlinear Partial Differential Equations, Second Edition takes a more practical approach to nonlinear PDEs by emphasizing how the results are used, why they are important, and how they are applied to real problems. The intertwining relationship between mathematics and physical phenomena is discovered using detailed examples of applications across various areas such as biology, combustion, traffic flow, heat transfer, fluid mechanics, quantum mechanics, and the chemical reactor theory. New features of the Second Edition also include: Additional intermediate-level exercises that facilitate the development of advanced problem-solving skills New applications in the biological sciences, including age-structure, pattern formation, and the propagation of diseases An expanded bibliography that facilitates further investigation into specialized topics With individual, self-contained chapters and a broad scope of coverage that offers instructors the flexibility to design courses to meet specific objectives, An Introduction to Nonlinear Partial Differential Equations, Second Edition is an ideal text for applied mathematics courses at the upper-undergraduate and graduate levels. It also serves as a valuable resource for researchers and professionals in the fields of mathematics, biology, engineering, and physics who would like to further their knowledge of PDEs.

Spatial Patterns

Author : L.A. Peletier
Publisher : Springer Science & Business Media
ISBN 13 : 1461201357
Total Pages : 347 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Spatial Patterns by : L.A. Peletier

Download or read book Spatial Patterns written by L.A. Peletier and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of spatial patterns in extended systems, and their evolution with time, poses challenging questions for physicists and mathematicians alike. Waves on water, pulses in optical fibers, periodic structures in alloys, folds in rock formations, and cloud patterns in the sky: patterns are omnipresent in the world around us. Their variety and complexity make them a rich area of study. In the study of these phenomena an important role is played by well-chosen model equations, which are often simpler than the full equations describing the physical or biological system, but still capture its essential features. Through a thorough analysis of these model equations one hopes to glean a better under standing of the underlying mechanisms that are responsible for the formation and evolution of complex patterns. Classical model equations have typically been second-order partial differential equations. As an example we mention the widely studied Fisher-Kolmogorov or Allen-Cahn equation, originally proposed in 1937 as a model for the interaction of dispersal and fitness in biological populations. As another example we mention the Burgers equation, proposed in 1939 to study the interaction of diffusion and nonlinear convection in an attempt to understand the phenomenon of turbulence. Both of these are nonlinear second-order diffusion equations.

Lectures on Nonlinear Hyperbolic Differential Equations

Author : Lars Hörmander
Publisher : Springer Science & Business Media
ISBN 13 : 9783540629214
Total Pages : 308 pages
Book Rating : 4.6/5 (292 download)

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Book Synopsis Lectures on Nonlinear Hyperbolic Differential Equations by : Lars Hörmander

Download or read book Lectures on Nonlinear Hyperbolic Differential Equations written by Lars Hörmander and published by Springer Science & Business Media. This book was released on 1997-07-17 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this introductory textbook, a revised and extended version of well-known lectures by L. Hörmander from 1986, four chapters are devoted to weak solutions of systems of conservation laws. Apart from that the book only studies classical solutions. Two chapters concern the existence of global solutions or estimates of the lifespan for solutions of nonlinear perturbations of the wave or Klein-Gordon equation with small initial data. Four chapters are devoted to microanalysis of the singularities of the solutions. This part assumes some familiarity with pseudodifferential operators which are standard in the theory of linear differential operators, but the extension to the more exotic classes of opertors needed in the nonlinear theory is presented in complete detail.

Non-Linear Differential Equations and Dynamical Systems

Author : Luis Manuel Braga da Costa Campos
Publisher : CRC Press
ISBN 13 : 0429639619
Total Pages : 220 pages
Book Rating : 4.4/5 (296 download)

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Book Synopsis Non-Linear Differential Equations and Dynamical Systems by : Luis Manuel Braga da Costa Campos

Download or read book Non-Linear Differential Equations and Dynamical Systems written by Luis Manuel Braga da Costa Campos and published by CRC Press. This book was released on 2019-11-05 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Non-Linear Differential Equations and Dynamical Systems is the second book within Ordinary Differential Equations with Applications to Trajectories and Vibrations, Six-volume Set. As a set, they are the fourth volume in the series Mathematics and Physics Applied to Science and Technology. This second book consists of two chapters (chapters 3 and 4 of the set). The first chapter considers non-linear differential equations of first order, including variable coefficients. A first-order differential equation is equivalent to a first-order differential in two variables. The differentials of order higher than the first and with more than two variables are also considered. The applications include the representation of vector fields by potentials. The second chapter in the book starts with linear oscillators with coefficients varying with time, including parametric resonance. It proceeds to non-linear oscillators including non-linear resonance, amplitude jumps, and hysteresis. The non-linear restoring and friction forces also apply to electromechanical dynamos. These are examples of dynamical systems with bifurcations that may lead to chaotic motions. Presents general first-order differential equations including non-linear like the Ricatti equation Discusses differentials of the first or higher order in two or more variables Includes discretization of differential equations as finite difference equations Describes parametric resonance of linear time dependent oscillators specified by the Mathieu functions and other methods Examines non-linear oscillations and damping of dynamical systems including bifurcations and chaotic motions

Handbook of Nonlinear Partial Differential Equations, Second Edition

Author : Andrei D. Polyanin
Publisher : CRC Press
ISBN 13 : 142008724X
Total Pages : 1878 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Handbook of Nonlinear Partial Differential Equations, Second Edition by : Andrei D. Polyanin

Download or read book Handbook of Nonlinear Partial Differential Equations, Second Edition written by Andrei D. Polyanin and published by CRC Press. This book was released on 2016-04-19 with total page 1878 pages. Available in PDF, EPUB and Kindle. Book excerpt: New to the Second Edition More than 1,000 pages with over 1,500 new first-, second-, third-, fourth-, and higher-order nonlinear equations with solutions Parabolic, hyperbolic, elliptic, and other systems of equations with solutions Some exact methods and transformations Symbolic and numerical methods for solving nonlinear PDEs with MapleTM, Mathematica®, and MATLAB® Many new illustrative examples and tables A large list of references consisting of over 1,300 sources To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology. They outline the methods in a schematic, simplified manner and arrange the material in increasing order of complexity.

Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations

Author : Ivan Kiguradze
Publisher : Springer Science & Business Media
ISBN 13 : 9401118086
Total Pages : 343 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations by : Ivan Kiguradze

Download or read book Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations written by Ivan Kiguradze and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a comprehensive review of the developments which have taken place during the last thirty years concerning the asymptotic properties of solutions of nonautonomous ordinary differential equations. The conditions of oscillation of solutions are established, and some general theorems on the classification of equations according to their oscillatory properties are proved. In addition, the conditions are found under which nonlinear equations do not have singular, proper, oscillatory and monotone solutions. The book has five chapters: Chapter I deals with linear differential equations; Chapter II with quasilinear equations; Chapter III with general nonlinear differential equations; and Chapter IV and V deal, respectively, with higher-order and second-order differential equations of the Emden-Fowler type. Each section contains problems, including some which presently remain unsolved. The volume concludes with an extensive list of references. For researchers and graduate students interested in the qualitative theory of differential equations.