Nonlinear Analysis VOLUME 9

Covering a broad field of interest such as measure theory, functional analysis, and applied disciplines, this book features a variety of theoretical and applied methods. It provides recent results on critical point theory, nonlinear differential operators, and related regularity and comparison principles. It provides foundations of applied areas including boundary value problems, evolution equations, optimization, optimal control, and mechanics. Additional topics present Hausdorff theory, LeBesgue-Bochner and Sobolev spaces, and the spectral properties of the p-Laplacian. With a detailed bibliography and appendix, this is an accessible reference for graduate students and researchers.

Nonlinear analysis is a broad, interdisciplinary field characterized by a remarkable mixture of analysis, topology, and applications. Its concepts and techniques provide the tools for developing more realistic and accurate models for a variety of phenomena encountered in fields ranging from engineering and chemistry to economics and biology. This volume focuses on topics in nonlinear analysis pertinent to the theory of boundary value problems and their application in areas such as control theory and the calculus of variations. It complements the many other books on nonlinear analysis by addressing topics previously discussed fully only in scattered research papers. These include recent results on critical point theory, nonlinear differential operators, and related regularity and comparison principles. The rich variety of topics, both theoretical and applied, make Nonlinear Analysis useful to anyone, whether graduate student or researcher, working in analysis or its applications in optimal control, theoretical mechanics, or dynamical systems. An appendix contains all of the background material needed, and a detailed bibliography forms a guide for further study.

Hausdorff Measures and Capacity. Lebesgue-Bochner and Sobolev Spaces. Nonlinear Operators and Young Measures. Smooth and Nonsmooth Analysis and Variational Principles. Critical Point Theory. Eigenvalue Problems and Maximum Principles. Fixed Point Theory.