Existence of positive solutions for a semipositone boundary value problem on the half-line

Authors:
Ruyun Ma;Bao Zhu
Affiliations:
Department of Mathematics, Northwest Normal University, Lanzhou 730070, PR China;Department of Mathematics, Northwest Normal University, Lanzhou 730070, PR China
Venue:
Computers & Mathematics with Applications
Year:
2009

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Abstract

In this paper, we consider the boundary value problem on the half-line {x^''(t)-k^2(t)x(t)+@lm(t)f(t,x(t))=0,t@?(0,~),x(0)=0,limt-~x(t)=0, where k:[0,~)-(0,~) and f:[0,~)x[0,~)-R are continuous. We show the existence of positive solutions by using a fixed point theorem in cones.