Double solutions of three-point boundary-value problems for second-order differential equations

A double fixed point theorem is applied to yield the existence of at least two nonnegative solutions for the three-point boundary-value problem for a second-order differential equation, $$displaylines{ y'' + f(y)=0,quad 0 leq t leq 1,cr y(0) =0,quad y(p) - y(1) = 0, }$$ where $0$ less than $p$ less than $1$ is fixed, and $f:mathbb{R} o [0, infty)$ is continuous.