Periodic solutions of a second-order differential equation with one-sided growth restrictions on the restoring term (Q1116005)

This paper deals with the solvability (under Carathéodory sense) of the nonlinear periodic boundary value problem \(x''+h(x)=p(t),\) \(x(T)+x(0)=x'(T)-x'(0)=0\) \((T>0)\) where \(h: {\mathbb{R}}\to {\mathbb{R}}\) continuous, \(P: [0,T]\to {\mathbb{R}}\) Lebesgue integrable.