Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems: 1st Edition (Hardback) book cover

Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems

1st Edition

By Leszek Gasinski, Nikolaos S. Papageorgiou

Chapman and Hall/CRC

792 pages | 20 B/W Illus.

Purchasing Options:$ = USD
Hardback: 9781584884859
pub: 2004-07-27
$170.00
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Description

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 The presentation includes many recent results, including some that were previously unpublished.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 problems.

Reviews

"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. 2004

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

References

About the Series

Mathematical Analysis and Applications

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MAT003000
MATHEMATICS / Applied
MAT037000
MATHEMATICS / Functional Analysis
SCI040000
SCIENCE / Mathematical Physics