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This book focuses on nonlinear boundary value problems and the aspects of nonlinear analysis which are necessary to their study. The authors first give a comprehensive introduction to the many different classical methods from nonlinear analysis, variational principles, and Morse theory. They then provide a rigorous and detailed treatment of the relevant areas of nonlinear analysis with new applications to nonlinear boundary value problems for both ordinary and partial differential equations. Recent results on the existence and multiplicity of critical points for both smooth and nonsmooth functional, developments on the degree theory of monotone type operators, nonlinear maximum and comparison principles for p-Laplacian type operators, and new developments on nonlinear Neumann problems involving non-homogeneous differential operators appear for the first time in book form. The presentation is systematic, and an extensive bibliography and a remarks section at the end of each chapter highlight the text. This work will serve as an invaluable reference for researchers working in nonlinear analysis and partial differential equations as well as a useful tool for all those interested in the topics presented.
List of contents
Preface.- Introduction.- Sobolev Spaces.- Nonlinear Operators.- Nonsmooth Analysis.- Degree Theory.- Variational Principles and Critical Point Theory.- Morse Theory.- Bifurcation Theory.- Regularity Theorems and Maximum Principles.- Spectrum of Differential Operators.- Ordinary Differential Equations.- Nonlinear Elliptic Equations with Dirichlet Boundary Conditions.- Nonlinear Elliptic Equations with Neumann Boundary Conditions.- List of Symbols.- References.- Index .
Summary
This book focuses on nonlinear boundary value problems and the aspects of nonlinear analysis which are necessary to their study.
Additional text
From the book reviews:
“This volume is devoted to the qualitative analysis of some basic classes of nonlinear boundary value problems by means of modern variational and topological methods. … This material appears here for the first time in book form. The presentation is very clear and an extensive bibliography (397 titles) and a rich index highlight the text. This work will serve as a reference for researchers working in pure and applied nonlinear analysis.” (Vicenţiu D. Rădulescu, zbMATH, 2014)
Report
From the book reviews:
"This volume is devoted to the qualitative analysis of some basic classes of nonlinear boundary value problems by means of modern variational and topological methods. ... This material appears here for the first time in book form. The presentation is very clear and an extensive bibliography (397 titles) and a rich index highlight the text. This work will serve as a reference for researchers working in pure and applied nonlinear analysis." (Vicentiu D. Radulescu, zbMATH, 2014)
