Solvability of Nonlinear Singular Problems for Ordinary Differential Equations by Irena Rachunkova, Svatoslav Stanek, and Milan Tvrdy
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About this book :-
The book is addressed to researchers in related areas, to graduate students or advanced undergraduates, and, in particular, to those interested in singular and nonlinear boundary value problems. It can serve as a reference book on the existence theory for singular boundary value problems of ordinary differential equations as well as a textbook for graduate or undergraduate classes. The readers need basic knowledge of real analysis, linear and nonlinear functional analysis, theory of Lebesgue measure and integral, theory of ordinary differential equations (including the Carath´edory theory and boundary value problems) on the graduate level.
The monograph deals with boundary value problems which are considered in the frame of the Carath´eodory theory. If non linearities in differential equations fulfill the Carath´eodory conditions, the boundary value problems are called regular, while, if the Carath´eodory conditions are not fulfilled on the whole region, the problems are called singular. Two types of singularities are distinguished—time and space ones. For singular boundary value problems, we introduce notions of a solution and of a w-solution. Solutions of nth-order differential equations are understood as functions having absolutely continuous derivatives up to order n - 1 on the whole basic compact interval. On the other hand, w-solutions have these derivatives only locally absolutely continuous on a non compact subset of the basic interval. The main attention is paid to the existence of solutions of singular problems. The proofs are mostly based on regularization and sequential technique. The impact of our theoretical results is demonstrated by illustrative examples.
Book Detail :-
This book has following details information.
Title:
Solvability of Nonlinear Singular Problems for Ordinary Differential Equations by Irena Rachunkova, Svatoslav Stanek, and Milan Tvrdy by NA
Publisher:
Hindawi Publishing Corporation
Series:
FreeCompBooks
Year:
2009
Pages:
268
Type:
PDF
Language:
English
ISBN-10 #:
9774540409
ISBN-13 #:
978-9774540400
Country:
Pakistan
License:
N\A
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About Author :-
The author NA
NA
Book Contents :-
conver the following topics.
Higher-order singular problems - Existence principles for singular problems - Focal problems - (n, p) problem - Conjugate problem - Sturm-Liouville problem - Lidstone problem - Second-order singular problems with f-Laplacian - Dirichlet problem - Periodic problem - Mixed problem - Nonlocal problems - Problems with a parameter - Uniform integrability/equicontinuity - Convergence theorems - Some general existence theorems - Spectrum of the quasilinear Dirichlet problem
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