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Author : Yin Xi Huang
Publisher :
ISBN 13 :
Total Pages : 212 pages
Book Rating : 4.:/5 (657 download)
Download or read book Positive Global Solutions of Nonlinear Elliptic Equations written by Yin Xi Huang and published by . This book was released on 1989 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : David Lloyd Finn
Publisher :
ISBN 13 :
Total Pages : 394 pages
Book Rating : 4.:/5 (33 download)
Download or read book Positive Solutions to Nonlinear Elliptic Equations with Prescribed Singularities written by David Lloyd Finn and published by . This book was released on 1995 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Existence of Positive Solutions for Nonlinear Elliptic Equations with Convection Terms written by and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : W.-M. Ni
Publisher : Springer Science & Business Media
ISBN 13 : 1461396050
Total Pages : 359 pages
Book Rating : 4.4/5 (613 download)
Download or read book Nonlinear Diffusion Equations and Their Equilibrium States I written by W.-M. Ni and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years considerable interest has been focused on nonlinear diffu sion problems, the archetypical equation for these being Ut = D.u + f(u). Here D. denotes the n-dimensional Laplacian, the solution u = u(x, t) is defined over some space-time domain of the form n x [O,T], and f(u) is a given real function whose form is determined by various physical and mathematical applications. These applications have become more varied and widespread as problem after problem has been shown to lead to an equation of this type or to its time-independent counterpart, the elliptic equation of equilibrium D.u + f(u) = o. Particular cases arise, for example, in population genetics, the physics of nu clear stability, phase transitions between liquids and gases, flows in porous media, the Lend-Emden equation of astrophysics, various simplified com bustion models, and in determining metrics which realize given scalar or Gaussian curvatures. In the latter direction, for example, the problem of finding conformal metrics with prescribed curvature leads to a ground state problem involving critical exponents. Thus not only analysts, but geome ters as well, can find common ground in the present work. The corresponding mathematical problem is to determine how the struc ture of the nonlinear function f(u) influences the behavior of the solution.
Author : Luis A. Caffarelli
Publisher : American Mathematical Soc.
ISBN 13 : 0821804375
Total Pages : 114 pages
Book Rating : 4.8/5 (218 download)
Download or read book Fully Nonlinear Elliptic Equations written by Luis A. Caffarelli and published by American Mathematical Soc.. This book was released on 1995 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the book is to extend classical regularity theorems for solutions of linear elliptic partial differential equations to the context of fully nonlinear elliptic equations. This class of equations often arises in control theory, optimization, and other applications. The authors give a detailed presentation of all the necessary techniques. Instead of treating these techniques in their greatest generality, they outline the key ideas and prove the results needed for developing the subsequent theory. Topics discussed in the book include the theory of viscosity solutions for nonlinear equations, the Alexandroff estimate and Krylov-Safonov Harnack-type inequality for viscosity solutions, uniqueness theory for viscosity solutions, Evans and Krylov regularity theory for convex fully nonlinear equations, and regularity theory for fully nonlinear equations with variable coefficients.
Author :
Publisher :
ISBN 13 :
Total Pages : 143 pages
Book Rating : 4.:/5 (931 download)
Download or read book Positive Solutions to Nonlinear Elliptic Equations with Critical Potential written by and published by . This book was released on 2006 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Philip Korman
Publisher : World Scientific
ISBN 13 : 9814374350
Total Pages : 254 pages
Book Rating : 4.8/5 (143 download)
Download or read book Global Solution Curves for Semilinear Elliptic Equations written by Philip Korman and published by World Scientific. This book was released on 2012 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the bifurcation theory approach to global solution curves and studies the exact multiplicity of solutions for semilinear Dirichlet problems, aiming to obtain a complete understanding of the solution set. This understanding opens the way to efficient computation of all solutions. Detailed results are obtained in case of circular domains, and some results for general domains are also presented. The author is one of the original contributors to the field of exact multiplicity results.
Author : Philip Korman
Publisher : World Scientific
ISBN 13 : 9814458066
Total Pages : 254 pages
Book Rating : 4.8/5 (144 download)
Download or read book Global Solution Curves For Semilinear Elliptic Equations written by Philip Korman and published by World Scientific. This book was released on 2012-02-10 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the bifurcation theory approach to global solution curves and studies the exact multiplicity of solutions for semilinear Dirichlet problems, aiming to obtain a complete understanding of the solution set. This understanding opens the way to efficient computation of all solutions. Detailed results are obtained in case of circular domains, and some results for general domains are also presented.The author is one of the original contributors to the field of exact multiplicity results.
Author : Alexander A. Kovalevsky
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110390086
Total Pages : 531 pages
Book Rating : 4.1/5 (13 download)
Download or read book Singular Solutions of Nonlinear Elliptic and Parabolic Equations written by Alexander A. Kovalevsky and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-03-21 with total page 531 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph looks at several trends in the investigation of singular solutions of nonlinear elliptic and parabolic equations. It discusses results on the existence and properties of weak and entropy solutions for elliptic second-order equations and some classes of fourth-order equations with L1-data and questions on the removability of singularities of solutions to elliptic and parabolic second-order equations in divergence form. It looks at localized and nonlocalized singularly peaking boundary regimes for different classes of quasilinear parabolic second- and high-order equations in divergence form. The book will be useful for researchers and post-graduate students that specialize in the field of the theory of partial differential equations and nonlinear analysis. Contents: Foreword Part I: Nonlinear elliptic equations with L^1-data Nonlinear elliptic equations of the second order with L^1-data Nonlinear equations of the fourth order with strengthened coercivity and L^1-data Part II: Removability of singularities of the solutions of quasilinear elliptic and parabolic equations of the second order Removability of singularities of the solutions of quasilinear elliptic equations Removability of singularities of the solutions of quasilinear parabolic equations Quasilinear elliptic equations with coefficients from the Kato class Part III: Boundary regimes with peaking for quasilinear parabolic equations Energy methods for the investigation of localized regimes with peaking for parabolic second-order equations Method of functional inequalities in peaking regimes for parabolic equations of higher orders Nonlocalized regimes with singular peaking Appendix: Formulations and proofs of the auxiliary results Bibliography
Author : Messoud Efendiev
Publisher : Springer
ISBN 13 : 3319984071
Total Pages : 273 pages
Book Rating : 4.3/5 (199 download)
Download or read book Symmetrization and Stabilization of Solutions of Nonlinear Elliptic Equations written by Messoud Efendiev and published by Springer. This book was released on 2018-10-17 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with a systematic study of a dynamical system approach to investigate the symmetrization and stabilization properties of nonnegative solutions of nonlinear elliptic problems in asymptotically symmetric unbounded domains. The usage of infinite dimensional dynamical systems methods for elliptic problems in unbounded domains as well as finite dimensional reduction of their dynamics requires new ideas and tools. To this end, both a trajectory dynamical systems approach and new Liouville type results for the solutions of some class of elliptic equations are used. The work also uses symmetry and monotonicity results for nonnegative solutions in order to characterize an asymptotic profile of solutions and compares a pure elliptic partial differential equations approach and a dynamical systems approach. The new results obtained will be particularly useful for mathematical biologists.
Author : 平田潤
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (836 download)
Download or read book Positive Solutions of Nonlinear Elliptic Equations with G-symmetry written by 平田潤 and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Haim Brezis
Publisher :
ISBN 13 :
Total Pages : 41 pages
Book Rating : 4.:/5 (227 download)
Download or read book Positive Solutions of Nonlinear Elliptic Equations Involving Critical Sobolev Exponents written by Haim Brezis and published by . This book was released on 1983 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Alexandre N. Carvalho
Publisher : Birkhäuser
ISBN 13 : 3319199021
Total Pages : 434 pages
Book Rating : 4.3/5 (191 download)
Download or read book Contributions to Nonlinear Elliptic Equations and Systems written by Alexandre N. Carvalho and published by Birkhäuser. This book was released on 2015-11-14 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of contributions pays tribute to the life and work of Djairo Guedes de Figueiredo on the occasion of his 80th birthday. The articles it contains were born out of the ICMC Summer Meeting on Differential Equations – 2014 Chapter, also dedicated to de Figueiredo and held at the Universidade de São Paulo at São Carlos, Brazil from February 3-7, 2014. The contributing authors represent a group of international experts in the field and discuss recent trends and new directions in nonlinear elliptic partial differential equations and systems. Djairo Guedes de Figueiredo has had a very active scientific career, publishing 29 monographs and over one hundred research articles. His influence on Brazilian mathematics has made him one of the pillars of the subject in that country. He had a major impact on the development of analysis, especially in its application to nonlinear elliptic partial differential equations and systems throughout the entire world. The articles collected here pay tribute to him and his legacy and are intended for graduate students and researchers in mathematics and related areas who are interested in nonlinear elliptic partial differential equations and systems.
Author : Vicentiu D. Radulescu
Publisher : Hindawi Publishing Corporation
ISBN 13 : 9774540395
Total Pages : 205 pages
Book Rating : 4.7/5 (745 download)
Download or read book Qualitative Analysis of Nonlinear Elliptic Partial Differential Equations written by Vicentiu D. Radulescu and published by Hindawi Publishing Corporation. This book was released on 2008 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive introduction to the mathematical theory of nonlinear problems described by elliptic partial differential equations. These equations can be seen as nonlinear versions of the classical Laplace equation, and they appear as mathematical models in different branches of physics, chemistry, biology, genetics, and engineering and are also relevant in differential geometry and relativistic physics. Much of the modern theory of such equations is based on the calculus of variations and functional analysis. Concentrating on single-valued or multivalued elliptic equations with nonlinearities of various types, the aim of this volume is to obtain sharp existence or nonexistence results, as well as decay rates for general classes of solutions. Many technically relevant questions are presented and analyzed in detail. A systematic picture of the most relevant phenomena is obtained for the equations under study, including bifurcation, stability, asymptotic analysis, and optimal regularity of solutions. The method of presentation should appeal to readers with different backgrounds in functional analysis and nonlinear partial differential equations. All chapters include detailed heuristic arguments providing thorough motivation of the study developed later on in the text, in relationship with concrete processes arising in applied sciences. A systematic description of the most relevant singular phenomena described in this volume includes existence (or nonexistence) of solutions, unicity or multiplicity properties, bifurcation and asymptotic analysis, and optimal regularity. The book includes an extensive bibliography and a rich index, thus allowing for quick orientation among the vast collection of literature on the mathematical theory of nonlinear phenomena described by elliptic partial differential equations.
Author : Marco Squassina
Publisher :
ISBN 13 :
Total Pages : 14 pages
Book Rating : 4.:/5 (59 download)
Download or read book On the Existence of Positive Entire Solutions of Nonlinear Elliptic Equations written by Marco Squassina and published by . This book was released on 2000 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : I. V. Skrypnik
Publisher : American Mathematical Soc.
ISBN 13 : 9780821897560
Total Pages : 370 pages
Book Rating : 4.8/5 (975 download)
Download or read book Methods for Analysis of Nonlinear Elliptic Boundary Value Problems written by I. V. Skrypnik and published by American Mathematical Soc.. This book was released on 1994-01-01 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of nonlinear elliptic equations is currently one of the most actively developing branches of the theory of partial differential equations. This book investigates boundary value problems for nonlinear elliptic equations of arbitrary order. In addition to monotone operator methods, a broad range of applications of topological methods to nonlinear differential equations is presented: solvability, estimation of the number of solutions, and the branching of solutions of nonlinear equations. Skrypnik establishes, by various procedures, a priori estimates and the regularity of solutions of nonlinear elliptic equations of arbitrary order. Also covered are methods of homogenization of nonlinear elliptic problems in perforated domains. The book is suitable for use in graduate courses in differential equations and nonlinear functional analysis.
Author : Monica Lazzo
Publisher :
ISBN 13 :
Total Pages : 9 pages
Book Rating : 4.:/5 (246 download)
Download or read book Multiple Positive Solutions on Nonlinear Elliptic Equations Involving Critical Sobolev Exponents written by Monica Lazzo and published by . This book was released on 1991 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt:
