Generalized Topological Degree and Semilinear Equations
Part of Cambridge Tracts in Mathematics
- Author: Wolodymyr V. Petryshyn, Rutgers University, New Jersey
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.Read more
- For graduate students in maths, applied maths and physics
- Can be used as a text for graduate courses in nonlinear analysis
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'The book presents new and well-known results in a unified approach.' European Mathematical Society Newsletter
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- Date Published: April 2011
- format: Adobe eBook Reader
- isbn: 9780511890727
- availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
1. Introduction to the Brouwer and Leray–Schauder degrees, A-proper mappings, and linear theory
2. Generalized degree for densely defined A-proper mappings with some applications to semi-linear equations
3. Solvability of periodic semi-linear ODEs at resonance
4. Semi-constructive solvability, existence theorems, structure of the solution set
5. Solvability of semi-linear PDEs at resonance.
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