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Boundary Value Problems for Singular Second-Order Functional Differential Equations

Boundary Value Problems for Singular Second-Order Functional Differential Equations Positive solutions to the boundary value problem, $$ \left\{ {\begin{array}{*{20}l} {{{y}\ifmmode{''}\else$''$\fi = - f{\left( {x,y{\left( {w{\left( x \right)}} \right)}} \right)},} \hfill} & {{0 < x < 1,} \hfill} \\ {{\alpha y{\left( x \right)} - \beta {y}\ifmmode{'}\else$'$\fi{\left( x \right)} = \xi {\left( x \right)},} \hfill} & {{a \leqslant x \leqslant 0,} \hfill} \\ {{\gamma y{\left( x \right)} + \delta {y}\ifmmode{'}\else$'$\fi{\left( x \right)} = \eta {\left( x \right)},} \hfill} & {{1 \leqslant x \leqslant b,} \hfill} \\ \end{array} } \right. $$ are obtained by applying the Schauder fixed point theorem, where w(x) is a continuous function defined on [0, 1] and f(x, y) is a function defined on (0, 1)×(0, ∞), which satisfies certain restrictions and may have singularity at y=0. The result corrects and improves an existence theorem due to Erbe and Kong[1]. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Boundary Value Problems for Singular Second-Order Functional Differential Equations

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Publisher
Springer Journals
Copyright
Copyright © 2002 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s102550200023
Publisher site
See Article on Publisher Site

Abstract

Positive solutions to the boundary value problem, $$ \left\{ {\begin{array}{*{20}l} {{{y}\ifmmode{''}\else$''$\fi = - f{\left( {x,y{\left( {w{\left( x \right)}} \right)}} \right)},} \hfill} & {{0 < x < 1,} \hfill} \\ {{\alpha y{\left( x \right)} - \beta {y}\ifmmode{'}\else$'$\fi{\left( x \right)} = \xi {\left( x \right)},} \hfill} & {{a \leqslant x \leqslant 0,} \hfill} \\ {{\gamma y{\left( x \right)} + \delta {y}\ifmmode{'}\else$'$\fi{\left( x \right)} = \eta {\left( x \right)},} \hfill} & {{1 \leqslant x \leqslant b,} \hfill} \\ \end{array} } \right. $$ are obtained by applying the Schauder fixed point theorem, where w(x) is a continuous function defined on [0, 1] and f(x, y) is a function defined on (0, 1)×(0, ∞), which satisfies certain restrictions and may have singularity at y=0. The result corrects and improves an existence theorem due to Erbe and Kong[1].

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jan 1, 2002

References