Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4632282 | Applied Mathematics and Computation | 2010 | 8 Pages |
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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Xinguang Zhang, Lishan Liu,