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Multiple Positive Solutions For Classes Of Elliptic Systems With Combined Nonlinear Effects
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Book Synopsis Multiple Positive Solutions for Classes of Elliptic Systems with Combined Nonlinear Effects by : Jaffar Ali
Download or read book Multiple Positive Solutions for Classes of Elliptic Systems with Combined Nonlinear Effects written by Jaffar Ali and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We study positive solutions to nonlinear elliptic systems of the form: \begin{eqnarray*} -\Delta u =\lambda f(v) \mbox{ in }\Omega\\ -\Delta v =\lambda g(u) \mbox{ in }\Omega\\ \quad~~ u=0=v \mbox{ on }\partial\Omega \end{eqnarray*} where $ \Delta u $ is the Laplacian of $ u $, $ \lambda $ is a positive parameter and $ \Omega $ is a bounded domain in $ R^n $ with smooth boundary $ partial\Omega $. In particular, we will analyze the combined effects of the nonlinearities on the existence and multiplicity of positive solutions. We also study systems with multiparameters and stronger coupling. We extend our results to $ p $ - $ q $ -Laplacian systems and to $ n\times n $ systems. We mainly use sub- and super-solutions to prove our results.
Book Synopsis MULTIPLE POSITIVE SOLUTIONS FOR CLASSES OF ELLIPTIC SYSTEMS WITH COMBINED NONLINEAR EFFECTS. by :
Download or read book MULTIPLE POSITIVE SOLUTIONS FOR CLASSES OF ELLIPTIC SYSTEMS WITH COMBINED NONLINEAR EFFECTS. written by and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We study positive solutions to nonlinear elliptic systems of the form: \begin{eqnarray*} -\Delta u =\lambda f(v) \mbox{ in }\Omega\\ -\Delta v =\lambda g(u) \mbox{ in }\Omega\\ \quad~~ u=0=v \mbox{ on }\partial\Omega \end{eqnarray*} where $\Delta u$ is the Laplacian of $u$, $\lambda$ is a positive parameter and $\Omega$ is a bounded domain in $R^n$ with smooth boundary $\partial\Omega$. In particular, we will analyze the combined effects of the nonlinearities on the existence and multiplicity of positive solutions. We also study systems with multiparameters and stronger coupling. We extend our results to $p$-$q$-Laplacian systems and to $n\times n$ systems. We mainly use sub- and super-solutions to prove our results.
Book Synopsis Multiple Positive Solutions on Nonlinear Elliptic Equations Involving Critical Sobolev Exponents by : Monica Lazzo
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:
Book Synopsis Existence and Non-existence of Positive Solutions of Non-linear Elliptic Systems and the Bi-harmonic Equation by : Lambertus A. Peletier
Download or read book Existence and Non-existence of Positive Solutions of Non-linear Elliptic Systems and the Bi-harmonic Equation written by Lambertus A. Peletier and published by . This book was released on 1991 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Optimization of Elliptic Systems by : Pekka Neittaanmaki
Download or read book Optimization of Elliptic Systems written by Pekka Neittaanmaki and published by Springer Science & Business Media. This book was released on 2007-01-04 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present monograph is intended to provide a comprehensive and accessible introduction to the optimization of elliptic systems. This area of mathematical research, which has many important applications in science and technology. has experienced an impressive development during the past two decades. There are already many good textbooks dealing with various aspects of optimal design problems. In this regard, we refer to the works of Pironneau [1984], Haslinger and Neittaanmaki [1988], [1996], Sokolowski and Zolksio [1992], Litvinov [2000], Allaire [2001], Mohammadi and Pironneau [2001], Delfour and Zolksio [2001], and Makinen and Haslinger [2003]. Already Lions [I9681 devoted a major part of his classical monograph on the optimal control of partial differential equations to the optimization of elliptic systems. Let us also mention that even the very first known problem of the calculus of variations, the brachistochrone studied by Bernoulli back in 1696. is in fact a shape optimization problem. The natural richness of this mathematical research subject, as well as the extremely large field of possible applications, has created the unusual situation that although many important results and methods have already been est- lished, there are still pressing unsolved questions. In this monograph, we aim to address some of these open problems; as a consequence, there is only a minor overlap with the textbooks already existing in the field.
Download or read book Mathematical Reviews written by and published by . This book was released on 2007 with total page 1164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Differential and Integral Equations by :
Download or read book Differential and Integral Equations written by and published by . This book was released on 2007 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nonlinear Partial Differential Equations and Free Boundaries: Elliptic equations by : J. I. Díaz
Download or read book Nonlinear Partial Differential Equations and Free Boundaries: Elliptic equations written by J. I. Díaz and published by . This book was released on 1985 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this Research Note the author brings together the body of known work and presents many recent results relating to nonlinear partial differential equations that give rise to a free boundary--usually the boundary of the set where the solution vanishes identically. The formation of such a boundary depends on an adequate balance between two of the terms of the equation that represent the particular characteristics of the phenomenon under consideration: diffusion, absorption, convection, evolution etc. These balances do not occur in the case of a linear equation or an arbitrary nonlinear equation. Their characterization is studied for several classes of nonlinear equations relating to applications such as chemical reactions, non-Newtonian fluids, flow through porous media and biological populations. In this first volume, the free boundary for nonlinear elliptic equations is discussed. A second volume dealing with parabolic and hyperbolic equations is in preparation.
Book Synopsis Analysis and Computation of Multiple Unstable Solutions to Nonlinear Elliptic Systems by : Xianjin Chen
Download or read book Analysis and Computation of Multiple Unstable Solutions to Nonlinear Elliptic Systems written by Xianjin Chen and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We study computational theory and methods for finding multiple unstable solutions (corresponding to saddle points) to three types of nonlinear variational elliptic systems: cooperative, noncooperative, and Hamiltonian. We first propose a new Lorthogonal selection in a product Hilbert space so that a solution manifold can be defined. Then, we establish, respectively, a local characterization for saddle points of finite Morse index and of infinite Morse index. Based on these characterizations, two methods, called the local min-orthogonal method and the local min-max-orthogonal method, are developed and applied to solve those three types of elliptic systems for multiple solutions. Under suitable assumptions, a subsequence convergence result is established for each method. Numerical experiments for different types of model problems are carried out, showing that both methods are very reliable and efficient in computing coexisting saddle points or saddle points of infinite Morse index. We also analyze the instability of saddle points in both single and product Hilbert spaces. In particular, we establish several estimates of the Morse index of both coexisting and non-coexisting saddle points via the local min-orthogonal method developed and propose a local instability index to measure the local instability of both degenerate and nondegenerate saddle points. Finally, we suggest two extensions of an L-orthogonal selection for future research so that multiple solutions to more general elliptic systems such as nonvariational elliptic systems may also be found in a stable way.
Book Synopsis The Existence of Positive Solutions for Semilinear Elliptic System by : Wang Mingxin
Download or read book The Existence of Positive Solutions for Semilinear Elliptic System written by Wang Mingxin and published by . This book was released on 1990 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Existence of Positive Solutions for Nonlinear Elliptic Equations with Convection Terms by :
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:
Book Synopsis Pairs of Positive Solutions on Nonlinear Elliptic Partial Differential Equations by : P. H. Rabinowitz
Download or read book Pairs of Positive Solutions on Nonlinear Elliptic Partial Differential Equations written by P. H. Rabinowitz and published by . This book was released on 1972 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Positive Solutions of Semilinear Elliptic Systems by : Ph Clément
Download or read book Positive Solutions of Semilinear Elliptic Systems written by Ph Clément and published by . This book was released on 1991 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Qualitative Analysis of Nonlinear Elliptic Partial Differential Equations by : Vicentiu D. Radulescu
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.
Book Synopsis On the Rugularity of Weak Solutions to Nonlinear Elliptic Systems of Partial Differential Equations by : Jindrich Nec̆as
Download or read book On the Rugularity of Weak Solutions to Nonlinear Elliptic Systems of Partial Differential Equations written by Jindrich Nec̆as and published by . This book was released on 1979 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Del Pezzo Surfaces of Degree Four by : Boris E. Kunyavskiĭ
Download or read book Del Pezzo Surfaces of Degree Four written by Boris E. Kunyavskiĭ and published by . This book was released on 1989 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Dissertation Abstracts International by :
Download or read book Dissertation Abstracts International written by and published by . This book was released on 2009 with total page 810 pages. Available in PDF, EPUB and Kindle. Book excerpt:
