The Duffing equation with the potential Landesman–Lazer condition

In this paper we investigate the nonlinear second-order ordinary differential equation at resonance u″(x)+cu′+(m2−c24)u+g(x,u)=f(x),x∈〈0,π〉,x(0)=x(π)=0.x(0)=x(π)=0. We suppose that the nonlinearity gg satisfies a potential Landesman–Lazer condition and we prove the existence of a solution to this problem using a saddle point theorem.