Article ID Journal Published Year Pages File Type
4632282 Applied Mathematics and Computation 2010 8 Pages PDF
Abstract

In this paper, we concert with the existence of positive solution for the following nonlinear singular differential system with four-point boundary conditions-x″=f(t,y),-y″=g(t,x),αx(0)-βx′(0)=δx(1)+γx′(1)=0,y(0)=ay(ξ1),y(1)=by(ξ2),where 0<ξ1<ξ2<1,α,β,δ,γ,a,b0<ξ1<ξ2<1,α,β,δ,γ,a,b are nonnegative constants such that ρ=βγ+αγ+αδ>0ρ=βγ+αγ+αδ>0. By structuring upper and lower solution and using Schauder fixed point theorem, a necessary and sufficient condition for the existence of positive solutions is established. An example is worked out to illustrate our main result.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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