Titlebook: An Introduction to Nonlinear Functional Analysis and Elliptic Problems; Antonio Ambrosetti,David Arcoya Textbook 2011 Springer Science+Bus

Apoptosis

Preliminaries,In this chapter we collect some preliminary results that we will use throughout the rest of the book, such as Fréechet derivatives, superposition operators and eak and classical solutions of linear elliptic equations and their eigenvalues. Sobolev function spaces are also outlined, although a more complete treatment is postponed until Appendix A.

粗野

Inflamed

,Leray—Schauder Topological Degree,To study the number of solutions of equations like.where Ω is an open set in a Banach space ., . and ., and based on a similar idea of Brouwer for continuous maps defined in finite-dimensional spaces, Leray and Schauder [64] introduced a topological tool, called the degree.

极端的正确性

An Outline of Critical Points,This chapter deals with variational methods. In addition to the existence of minima of a functional, we discuss the mountain pass theorem, and the linking theorem which are used to find saddle points. A perturbation method, variational in nature, is studied in the last section.

Crumple

Dictation

Elliptic Problems and Functional Analysis,The purpose of this chapter is to show how a nonlinear elliptic problem can be transformed into an operator equation that can be treated with the abstract tools discussed in the previous chapters.

似少年

Asymmetric Nonlinearities,This chapter deals with nonlinear problems with nonlinearities whose behavior at +∞ and −∞ jumps through an eigenvalue of the linear part.

AORTA

Stationary States of Evolution Equations,This final chapter deals with the existence of ground and bound states of nonlinear Schrödinger (NLS) equations. Semiclassical states are discussed in Sect. 13.2. Systems of coupled NLS equations are handled in Sects. 13.3 and 13.4.

Pamphlet

Antonio Ambrosetti,David ArcoyaProvides the basic, abstract tools used in nonlinear analysis.Key results such as the Banach contraction principle, a fixed point theorem for increasing operators, local and global inversion theory, L

depreciate

Progress in Nonlinear Differential Equations and Their Applicationshttp://image.papertrans.cn/a/image/155396.jpg