Positive solutions of three-point boundary value problems for systems of nonlinear second order ordinary differential equations

In this paper, we study the three-point boundary value problems for systems of nonlinear second order ordinary differential equations of the form{−u″=f(t,v),t∈(0,1),−v″=g(t,u),t∈(0,1),u(0)=v(0)=0,αu(η)=u(1),αv(η)=v(1). Under some conditions, we show the existence and multiplicity of positive solutions of the above problem by applying the fixed point index theory in cones.