Positive solutions for the nonhomogeneous three-point boundary value problem of second-order differential equations

Authors:
Haibo Chen
Affiliations:
Department of Mathematics, Central South University, Changsha, 410075, PR China and Mathematical Institute, University of Oxford, OX1 3LB, UK
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2007

Citing 2
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Abstract

This paper is concerned with the existence of positive solutions to the nonhomogeneous three-point boundary value problem of the second-order ordinary differential equation u^''(t)+a(t)u^'(t)+b(t)u(t)+h(t)f(u)=0u(0)=0,u(1)-@au(@h)=b where 00, and f@?C([0,~),[0,~)). By applying Krasnosel'skii's fixed-point theorem in Banach spaces, some sufficient conditions guaranteeing the existence of at least one positive solution if f is either superlinear or sublinear are established for the above boundary value problem. The results obtained extend and complement some known results.