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

790 pages

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 The presentation includes many recent results, including some that were previously unpublished.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

Table of Contents

Mathematical Background. Critical Point Theory. Ordinary Differential Equations. Elliptical Equations. Appendices: Set Theory and Topology. Measure Theory. Functional Analysis. Nonlinear Analysis.

About the Authors

Gasinski, Leszek; Papageorgiou, Nikolaos S.

About the Series

Mathematical Analysis and Applications

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Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Functional Analysis
SCIENCE / Mathematical Physics