Approximation-solvability of Nonlinear Functional and Differential Equations

1. Auflage 1992
ISBN: 978-0-8247-8793-6
Verlag: CRC Press

Buch, Englisch, 392 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 752 g

Reihe: Chapman & Hall/CRC Pure and Applied Mathematics

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.

Zielgruppe

Professional

Autoren/Hrsg.

Petryshyn, Wolodymyr V.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik

Inhaltsverzeichnis

Solvability of equations involving A-proper and pseudo-A-proper mappings; equations involving linear A-proper mappings; fixed points and surjectivity theorems for P-gamma-compact and A-proper-type maps; generalized degree for A-proper mappings and applications; solvability of PDEs and ODEs and bifurcation problems.

Über Autor(innen)

Petryshyn\, Wolodymyr V.