Existence of positive solutions for a nonlinear third-order ordinary differential equations

Abstract:

In this paper, by applying the fixed point theorem in cone, we study the existence of positive solutions of third-order four-point boundary value problemu'''(t)+f(t,u(t))=0,t∈[0,1],u'(0)=αu(ξ ),u'(1)+βu(η)=0,u''(0)=0,whereα，βare positive parameters,0≤ξ＜η≤1.Under some conditions on f,we obtained the existence of positive solutions of the problem (1.1)by estimating the upper bounds and lower bounds for kernel function.