Approximation-solvability of Nonlinear Functional and Differential Equations

By Wolodymyr Petryshyn and Petryshyn Petryshyn

Book 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.;Facilitating the understanding of the solvability of equations in infinite dimensional Banach space through finite dimensional appoximations, this book: offers an elementary introductions 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.

• Format: Paperback
• Language: English
• ISBN: 0367402572
• ISBN13: 9780367402570
• Release Date: September 2019
• Publisher: CRC Press
• Length: 392 Pages
• Weight: 1.25 lbs.
• Dimensions: 1.0" x 6.1" x 9.1"