Positive solutions of three-point boundary value problem for second order differential equations with an advanced argument (Q1423943)

Sufficient conditions are obtained for the existence of positive solutions to the three-point boundary value problem for a second-order differential equation with an advanced argument of the form \[ x''(t)+\lambda a(t)f(x(h(t)))=0,\quad t\in (0,1), \] with boundary conditions \(x(0)=0\), \(\alpha x(\eta)=x(1)\), where \(0<\eta<1\), \(0<\alpha<1/\eta\), \(\lambda>0\) and \(t\leq h(t)\leq1\). Krasnoselskii's fixed-point theorem for cones is used to establish the results.