an introduction to minimax theorems and their applications to differential equations nonconvex optimization and its applications

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An Introduction To Minimax Theorems And Their Applications To Differential Equations

Author : Maria do Rosário Grossinho
ISBN : 9781475733082
Genre : Mathematics
File Size : 81. 84 MB
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The book is intended to be an introduction to critical point theory and its applications to differential equations. Although the related material can be found in other books, the authors of this volume have had the following goals in mind: To present a survey of existing minimax theorems, To give applications to elliptic differential equations in bounded domains, To consider the dual variational method for problems with continuous and discontinuous nonlinearities, To present some elements of critical point theory for locally Lipschitz functionals and give applications to fourth-order differential equations with discontinuous nonlinearities, To study homoclinic solutions of differential equations via the variational methods. The contents of the book consist of seven chapters, each one divided into several sections. Audience: Graduate and post-graduate students as well as specialists in the fields of differential equations, variational methods and optimization.

Critical Point Theory And Its Applications

Author : Wenming Zou
ISBN : 9780387329680
Genre : Mathematics
File Size : 61. 30 MB
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This book presents some of the latest research in critical point theory, describing methods and presenting the newest applications. Coverage includes extrema, even valued functionals, weak and double linking, sign changing solutions, Morse inequalities, and cohomology groups. Applications described include Hamiltonian systems, Schrödinger equations and systems, jumping nonlinearities, elliptic equations and systems, superlinear problems and beam equations.

Multivalued Analysis And Nonlinear Programming Problems With Perturbations

Author : B. Luderer
ISBN : 9781475734683
Genre : Mathematics
File Size : 52. 27 MB
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The book presents a treatment of topological and differential properties of multivalued mappings and marginal functions. In addition, applications to sensitivity analysis of nonlinear programming problems under perturbations are studied. Properties of marginal functions associated with optimization problems are analyzed under quite general constraints defined by means of multivalued mappings. A unified approach to directional differentiability of functions and multifunctions forms the base of the volume. Nonlinear programming problems involving quasidifferentiable functions are considered as well. A significant part of the results are based on theories and concepts of two former Soviet Union researchers, Demyanov and Rubinov, and have never been published in English before. It contains all the necessary information from multivalued analysis and does not require special knowledge, but assumes basic knowledge of calculus at an undergraduate level.

Variational And Non Variational Methods In Nonlinear Analysis And Boundary Value Problems

Author : Dumitru Motreanu
ISBN : 9781475769210
Genre : Mathematics
File Size : 29. 53 MB
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This book reflects a significant part of authors' research activity dur ing the last ten years. The present monograph is constructed on the results obtained by the authors through their direct cooperation or due to the authors separately or in cooperation with other mathematicians. All these results fit in a unitary scheme giving the structure of this work. The book is mainly addressed to researchers and scholars in Pure and Applied Mathematics, Mechanics, Physics and Engineering. We are greatly indebted to Viorica Venera Motreanu for the careful reading of the manuscript and helpful comments on important issues. We are also grateful to our Editors of Kluwer Academic Publishers for their professional assistance. Our deepest thanks go to our numerous scientific collaborators and friends, whose work was so important for us. D. Motreanu and V. Radulescu IX Introduction The present monograph is based on original results obtained by the authors in the last decade. This book provides a comprehensive expo sition of some modern topics in nonlinear analysis with applications to the study of several classes of boundary value problems. Our framework includes multivalued elliptic problems with discontinuities, variational inequalities, hemivariational inequalities and evolution problems. The treatment relies on variational methods, monotonicity principles, topo logical arguments and optimization techniques. Excepting Sections 1 and 3 in Chapter 1 and Sections 1 and 3 in Chapter 2, the material is new in comparison with any other book, representing research topics where the authors contributed. The outline of our work is the following.

Nonsmooth Equations In Optimization

Author : Diethard Klatte
ISBN : 9781402005503
Genre : Mathematics
File Size : 66. 27 MB
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The book establishes links between regularity and derivative concepts of nonsmooth analysis and studies of solution methods and stability for optimization, complementarity and equilibrium problems. In developing necessary tools, it presents, in particular: an extended analysis of Lipschitz functions and the calculus of their generalized derivatives, including regularity, successive approximation and implicit functions for multivalued mappings; a unified theory of Lipschitzian critical points in optimization and other variational problems, with relations to reformulations by penalty, barrier and NCP functions; an analysis of generalized Newton methods based on linear and nonlinear approximations; the interpretation of hypotheses, generalized derivatives and solution methods in terms of original data and quadratic approximations; a rich collection of instructive examples and exercises.£/LIST£ Audience: Researchers, graduate students and practitioners in various fields of applied mathematics, engineering, OR and economics. Also university teachers and advanced students who wish to get insights into problems, future directions and recent developments.

Mathematical Reviews

Author :
ISBN : UOM:39015076649915
Genre : Mathematics
File Size : 49. 13 MB
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From Convexity To Nonconvexity

Author : R.P. Gilbert
ISBN : UOM:39015055859311
Genre : Mathematics
File Size : 43. 41 MB
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This collection of papers is dedicated to the memory of Gaetano Fichera, a great mathematician and also a good friend to the editors. Regrettably it took an unusual amount of time to bring this collection out. This was primarily due to the fact that the main editor who had collected all of the materials, for this volume, P. D. Panagiotopoulos, died unexpectedly during the period when we were editing the manuscript. The other two editors in appreciation of Panagiotopoulos' contribution to this field, believe it is therefore fitting that this collection be dedicated to his memory also. The theme of the collection is centered around the seminal research of G. Fichera on the Signorini problem. Variants on this idea enter in different ways. For example, by bringing in friction the problem is no longer self-adjoint and the minimization formulation is not valid. A large portion of this collection is devoted to survey papers concerning hemivariational methods, with a main point of its application to nonsmooth mechanics. Hemivariational inequali ties, which are a generalization of variational inequalities, were pioneered by Panagiotopoulos. There are many applications of this theory to the study of non convex energy functionals occurring in many branches of mechanics. An area of concentration concerns contact problems, in particular, quasistatic and dynamic contact problems with friction and damage. Nonsmooth optimization methods which may be divided into the main groups of subgradient methods and bundle methods are also discussed in this collection.

Minimax Theorems

Author : Michel Willem
ISBN : 0817639136
Genre : Mathematics
File Size : 59. 63 MB
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Willem's book is devoted to minimax theorems and their applications to partial diffential equations. Presenting basic minimax theorems in a simple and unified way, starting from a quantitative deformation lemma, the author gives many applications to problems dealing with lack of compactness, in particular, problems with critical exponents and existence pf solitary waves, The material covers many recent tools and some unpublished results, such as a treatment of the generalized Kadomtsev-Petviashvilli equation. It assumes only a basic knowledge of Soboleev spaces, partial differential equations and linear fuctional analysis. This book may serve as a textbook for advanced graduate students in partial differential equations. Contents Introduction 1. Mountain pass theorem 1.1 Differentiable functionals 1.2 Quantitative deformation lemma 1.3 Mountain pass theorem 1.4 Semilinear Dirichlet problem 1.5 Symmetry and compactness 1.6 Symmetric solitary waves 1.7 Subcritical Sobolev inequalities 1.8 Non symmetric solitary waves 1.9 Critical Sobolev inequality 1.10 Critical nonlinearities 2. Linking theorem 2.1 Quantitative deformation lemma 2.2 Ekeland variational principle 2.3 General minimax principle 2.4 Semilinear Dirichlet problem 2.5 Location theorem 2.6 Critical nonlinearities 3. Fountain theorem 3.1 Equivariant deformation 3.2 Fountain theorem 3.3 Semilinear Dirichlet problem 3.4 Multiple solitary waves 3.5 A dual theorem 3.6 Concave and convex nonlinearities 3.7 Concave and critical nonlinearities 4. Nehari manifold 4.1 Definition of Nehari manifold 4.2 Ground states 4.3 Properties of critical values 4.4 Nodal solutions 5. Relative category 5.1 Category 5.2 Relative category 5.3 Quantitative deformation lemma 5.4 Minimax theorem 5.5 Critical nonlinearities 6. Generalized linking theorem 6.1 Degree theory 6.2 Pseudogradient flow 6.3 Generalized linking theorem 6.4 Semilinear Schrodinger equation 7. Generalized Kadomtsev-Petviashvili equation 7.1 Definition of solitary waves 7.2 Functional setting 7.3 Existence of solitary waves 7.4 Variational identity 8. Representation of Palais-Smale sequences 8.1 Invariance by translations 8.2 Symmetric domains Appendix A: Superposition operator Appendix B: Variational identities Appendix C: Symmetry of minimizers Appendix D: Topological degree Bibliography Index of Notations Index Series: Progress in Nonlinear Differential Equations and Their Applications, Volume 24

Subject Guide To Books In Print

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ISBN : STANFORD:36105025888533
Genre : American literature
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American Book Publishing Record

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ISBN : STANFORD:36105111051640
Genre : Books
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