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Symmetric Positive Solutions for a Singular Second-Order Three-Point Boundary Value Problem

Symmetric Positive Solutions for a Singular Second-Order Three-Point Boundary Value Problem In this paper, we consider the following second-order three-point boundary value problem $$ \begin{array}{*{20}c} {{{u}\ifmmode{''}\else$''$\fi{\left( t \right)} + a{\left( t \right)}f{\left( {u{\left( t \right)}} \right)} = 0,}} & {{0 < t < 1,}} \\ {{u{\left( 0 \right)} - u{\left( 1 \right)} = 0,}} & {{{u}\ifmmode{'}\else$'$\fi{\left( 0 \right)} - {u}\ifmmode{'}\else$'$\fi{\left( 1 \right)} = u{\left( {1/2} \right)},}} \\ \end{array} $$ where a : (0, 1) → [0, ∞) is symmetric on (0, 1) and may be singular at t = 0 and t = 1, f : [0, ∞) → [0, ∞) is continuous. By using Krasnoselskii’s fixed point theorem in a cone, we get some existence results of positive solutions for the problem. The associated Green’s function for the three-point boundary value problem is also given. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Symmetric Positive Solutions for a Singular Second-Order Three-Point Boundary Value Problem

Sun, Yong-ping
Acta Mathematicae Applicatae Sinica , Volume 22 (1) – Jan 1, 2005
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References (15)

Publisher
Springer Journals
Copyright
Copyright © 2006 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/s10255-005-0286-z
Publisher site
See Article on Publisher Site

Abstract

In this paper, we consider the following second-order three-point boundary value problem $$ \begin{array}{*{20}c} {{{u}\ifmmode{''}\else$''$\fi{\left( t \right)} + a{\left( t \right)}f{\left( {u{\left( t \right)}} \right)} = 0,}} & {{0 < t < 1,}} \\ {{u{\left( 0 \right)} - u{\left( 1 \right)} = 0,}} & {{{u}\ifmmode{'}\else$'$\fi{\left( 0 \right)} - {u}\ifmmode{'}\else$'$\fi{\left( 1 \right)} = u{\left( {1/2} \right)},}} \\ \end{array} $$ where a : (0, 1) → [0, ∞) is symmetric on (0, 1) and may be singular at t = 0 and t = 1, f : [0, ∞) → [0, ∞) is continuous. By using Krasnoselskii’s fixed point theorem in a cone, we get some existence results of positive solutions for the problem. The associated Green’s function for the three-point boundary value problem is also given.

Journal

Acta Mathematicae Applicatae Sinica – Springer Journals

Published: Jan 1, 2005

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