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Multiple positive solutions for semi-positone m-point boundary value problems

Multiple positive solutions for semi-positone m-point boundary value problems In this article, we establish the existence of at least two positive solutions for the semi-positone m-point boundary value problem with a parameter $\begin{array}{*{20}c} {u''\left( t \right) + \lambda f\left( {t,u} \right) = 0} & {t \in \left( {0,1} \right),} \\ {u'\left( 0 \right) = \sum\limits_{i = 1}^{m - 2} {b_i u'} \left( {\xi _i } \right),} & {u\left( 1 \right) = \sum\limits_{i = 1}^{m - 2} {a_i u\left( {\xi _i } \right),} } \\ \end{array}$ where λ > 0 is a parameter, 0 < ξ 1 < ξ 2 < … < ξ m−2 < 1 with $0 < \sum\limits_{i = 1}^{m - 2} {a_i < 1, \sum\limits_{i = 1}^{m - 2} {b_i < 1, a_i , b_i \in \left[ {0,\infty } \right)} }$ and f(t, u) ≥ − M with M is a positive constant. The method employed is the Leggett-Williams fixed-point theorem. As an application, an example is given to demonstrate the main result. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Multiple positive solutions for semi-positone m-point boundary value problems

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Publisher
Springer Journals
Copyright
Copyright © 2011 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Theoretical, Mathematical and Computational Physics; Math Applications in Computer Science
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-009-6180-3
Publisher site
See Article on Publisher Site

Abstract

In this article, we establish the existence of at least two positive solutions for the semi-positone m-point boundary value problem with a parameter $\begin{array}{*{20}c} {u''\left( t \right) + \lambda f\left( {t,u} \right) = 0} & {t \in \left( {0,1} \right),} \\ {u'\left( 0 \right) = \sum\limits_{i = 1}^{m - 2} {b_i u'} \left( {\xi _i } \right),} & {u\left( 1 \right) = \sum\limits_{i = 1}^{m - 2} {a_i u\left( {\xi _i } \right),} } \\ \end{array}$ where λ > 0 is a parameter, 0 < ξ 1 < ξ 2 < … < ξ m−2 < 1 with $0 < \sum\limits_{i = 1}^{m - 2} {a_i < 1, \sum\limits_{i = 1}^{m - 2} {b_i < 1, a_i , b_i \in \left[ {0,\infty } \right)} }$ and f(t, u) ≥ − M with M is a positive constant. The method employed is the Leggett-Williams fixed-point theorem. As an application, an example is given to demonstrate the main result.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Nov 14, 2009

References