Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems

Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems

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Starting in the early 1980s, people using the tools of nonsmooth analysis developed some remarkable nonsmooth extensions of the existing critical point theory. Until now, however, no one had gathered these tools and results together into a unified, systematic survey of these advances. This book fills that gap. It provides a complete presentation of nonsmooth critical point theory, then goes beyond it to study nonlinear second order boundary value problems. The authors do not limit their treatment to problems in variational form. They also examine in detail equations driven by the p-Laplacian, its generalizations, and their spectral properties, studying a wide variety of problems and illustrating the powerful tools of modern nonlinear analysis. The presentation includes many recent results, including some that were previously unpublished. Detailed appendices outline the fundamental mathematical tools used in the book, and a rich bibliography forms a guide to the relevant literature. Most books addressing critical point theory deal only with smooth problems, linear or semilinear problems, or consider only variational methods or the tools of nonlinear operators. Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems offers a comprehensive treatment of the subject that is up-to-date, self-contained, and rich in methods for a wide variety of more

Product details

  • Hardback | 792 pages
  • 157.5 x 228.6 x 48.3mm | 1,156.67g
  • Taylor & Francis Ltd
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • New.
  • 20 black & white illustrations
  • 1584884851
  • 9781584884859

Review quote

"The book is as self-contained as possible and it is made more interesting by the perspectives in various sections, where the authors mention the historical background and development of the material and provide the reader with detailed explanations and updated references. [T]he book is very readable, and it can serve as a [starting] point for researchers and students [for] further investigations in the nonsmooth critical point theory as well as in its applications in mechanics, mathematical physics and engineering." - Studia Univ., Babes-Bolyai, Mathematica, Vol. XLIX, No. 3, Sept. 2004show more

Table of contents

MATHEMATICAL BACKGROUND Sobolev Spaces Set-Valued Analysis Nonsmooth Analysis Nonlinear Operators Elliptic Differential Equations Remarks CRITICAL POINT THEORY Locally Lipschitz Functionals Constrained Locally Lipschitz Functionals Perturbations of Locally Lipschitz Functionals Local Linking and Extensions Continuous Functionals Multivalued Functionals Remarks ORDINARY DIFFERENTIAL EQUATIONS Dirichlet Problems Periodic Problems Nonlinear Boundary Conditions Variational Methods Method of Upper and Lower Solutions Positive Solutions and Other Methods Hamiltonian Inclusions Remarks ELLIPTIC EQUATIONS Problems at Resonance Neumann Problems Problems with an Area-Type Term Strongly Nonlinear Problems Method of Upper and Lower Solutions Multiplicity Results Positive Solutions Problems with Discontinuous Nonlinearities Remarks APPENDIX Set Theory and Topology Measure Theory Functional Analysis Nonlinear Analysis List of Symbols Referencesshow more