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Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems: Mathematical Analysis and Applications

Autor Leszek Gasinski, Nikolaos S. Papageorgiou
en Limba Engleză Paperback – 23 oct 2019
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 The presentation includes many recent results, including some that were previously unpublished.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.
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Specificații

ISBN-13: 9780367394059
ISBN-10: 0367394057
Pagini: 790
Dimensiuni: 156 x 234 mm
Greutate: 1.46 kg
Ediția:1
Editura: CRC Press
Colecția Chapman and Hall/CRC
Seria Mathematical Analysis and Applications


Cuprins

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

Notă biografică

Gasinski, Leszek; Papageorgiou, Nikolaos S.

Descriere

Many important developments in nonsmooth critical point theory and in the analysis of nonlinear boundary value problems have emerged in the past 15 years, but to date, no book provides a survey of these advances. This book fills that gap. It provides a complete presentation of the nonsmooth critical point theory and investigates many different classes of boundary value problems, illustrating a variety of general methods. The treatment includes many important recent results, including some that were previously unpublished. Detailed appendices provide easy access to the mathematical tools used in the book, and a rich bibliography offers a guide to the literature.