Positive Solutions to System of Nonlinear Second-Order Three-Point Boundary Value Problem

Abstract

In this paper,we investigate the following system of nonlinear second-order three-point boundary value problems — u~" = f(t,v),t ∈(0,1),— v″ = g(t,u),t ∈(0,1),u(0) = αu(η),u(1) =βu(η),u(0) = av(η),v(1) = βv(η),where f,g ∈C([0,1]x R~+,R~+),g{t,0)≡ 0,η∈(0,1) and0 β≤α 1.First,Green's function for associated liner boundary value problem is constructed;next,several useful properties of the Green's function are obtained;in the last place,some existence and multiplicity criteria of positive solutions are established by using the fixed point theorems of cone expansion and compression.