This volume provides an introduction to modern concepts of linear and nlinear functional analysis. It may serve as a preparation for study of the abundant scientific literature on the theory of distributions, Sobolev spaces, elliptic equations and nlinear analysis. Its purpose is also to provide an insight into the variety of deeply interlaced mathematical tools applied in the study of nlinear problems. It starts with a review of the basics of Lebesgue spaces and Nemytzki operators. Special attention is paid to distributions, Sobelev spaces and their applications to the study of elliptic boundary value problems. Some of the methods of nlinear analysis are illustrated by: resonant and nresonant problems; lower semicontinuity and convexity; energy functionals; motone operators; reduction method; Landesman-Lazer problems; jumping nlinearities; the Mountain-Pass theorem; and topological degree. The book contains numerous examples and exercises, most with detailed solutions and hints.
Darko Zubrinic, Dragisa Mitrovic
Taylor & Francis Ltd
Date of Publication
Monographs and Surveys in Pure and Applied Mathematics