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.
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