Overview

This reference/text develops a constructive theory of solvability on linear and nonlinear abstract and differential equations - involving A-proper operator equations in separable Banach spaces, and treats the problem of existence of a solution for equations involving pseudo-A-proper and weakly-A-proper mappings, and illustrates their applications.

Key Features

Facilitating the understanding of the solvability of equations in infinite dimensional Banach space through finite dimensional approximations, this book:

• offers an elementary introduction to the general theory of A-proper and pseudo-A-proper maps;
• develops the linear theory of A-proper maps;
• furnishes the best possible results for linear equations;
• establishes the existence of fixed points and eigenvalues for P-gamma-compact maps, including classical results;
• provides surjectivity theorems for pseudo-A-proper and weakly-A-proper mappings that unify and extend earlier results on monotone and accretive mappings;
• shows how Friedrichs' linear extension theory can be generalized to the extensions of densely defined nonlinear operators in a Hilbert space;
• presents the generalized topological degree theory for A-proper mappings;
• and applies abstract results to boundary value problems and to bifurcation and asymptotic bifurcation problems.

There are also over 900 display equations, and an appendix that contains basic theorems from real function theory and measure/integration theory.