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

Abstract

In this paper, we study the three-point boundary value problems for systems of nonlinear second order ordinary differential equations of the form

$$\{\begin{array}{c}-u^{″}=f(t,v),t\in (0,1),\hfill \\ -v^{″}=g(t,u),t\in (0,1),\hfill \\ u(0)=v(0)=0,\alpha u(\eta )=u(1),\alpha v(\eta )=v(1).\hfill \end{array}$$

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.