Positive solutions to a second order three-point boundary value problem. (Q1408790)

The authors establish existence, nonexistence and multiplicity of nonnegative solutions to the following second-order differential equation \(-u''(t)=p(t)f(u(t))\), \(0<t<1\), subject to the boundary conditions \(u(0)=0\), \(u(1)-\alpha u(\beta)=\lambda\), where \(\beta\in (0,1),\alpha\in (0,\beta^{-1})\) and \(\lambda\) is a nonnegative parameter. The problem is transformed into a fixed-point problem for a completely continuous operator.