Generalized topological degree and semilinear equations / Wolodymyr V. Petryshyn.

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Introduction to the Brouwer and Leray-Schauder degrees, A-proper mappings, and linear theory -- Generalized degree for densely defined A-proper mappings, with some applications to semilinear equations -- Solvability of periodic semilinear ODEs at resonance -- Semiconstructive solvability, existence theorems, and structure of the solution set -- Solvability of semilinear PDEs at resonance.

This book describes many new results and extensions of the theory of generalised topological degree for densely defined A-proper operators and presents important applications, particularly to boundary value problems of non-linear ordinary and partial differential equations, which are intractable under any other existing theory. A-proper mappings arise naturally in the solution to an equation in infinite dimensional space via the finite dimensional approximation. This theory subsumes classical theory involving compact vector fields, as well as the more recent theories of condensing vector-fields, strongly monotone and strongly accretive maps. Researchers and graduate students in mathematics, applied mathematics and physics who make use of non-linear analysis will find this an important resource for new techniques.