Approximation-solvability of Nonlinear Functional and Differential Equations

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CRC Press, Dec 16, 1992 - Mathematics - 392 pages
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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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Contents

PREFACE
1
Further examples of Aproper mappings
20
Aproperness and the constructive solvability of some
34
Existence theorems and pseudoAproper mappings
49
I1 EQUATIONS INVOLVING LINEAR APROPER
55
Equations involving unbounded linear operators
64
Generalized Fredholm alternative
78
Constructive solvability of linear elliptic boundary
86
GENERALIZED DEGREE FOR APROPER
188
Singlevalued generalized degree for compact
212
Some applications of the generalized degree
219
Calculation of generalized degree
237
Bifurcation and asymptotic bifurcation for equations
250
SOLVABILITY OF PDEs AND ODEs
265
Solvability of ordinary differential equations
288
Approximationsolvability of periodic boundary value
304

Stability of projective methods and Aproperness
95
II1 FIXEDPOINT AND SURJECTIVITY THEOREMS
100
Constructive fixedpoint theorems for Pycompact
106
Constructive surjectivity theorems for PYcompact
121
Approximationsolvability and solvability of equations
127
Solvability of equations involving semilinear weakly
160
Variational BPs and ABPs for PDEs and ODEs
314
APPENDIX
323
REFERENCES
339
NOTATION
363
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