Approximation-solvability of nonlinear functional and differential equations
著者
書誌事項
Approximation-solvability of nonlinear functional and differential equations
（Monographs and textbooks in pure and applied mathematics, 171）
M. Dekker, c1993
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注記
Bibliography: p. 339-361
Includes index
内容説明・目次
内容説明
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.
目次
- 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.
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