Periodic solutions of nonlinear differential equations with double resonance (Q805844)

This paper deals with the periodic problem \(x''+g(t,x)=0,\) \(x(0)- x(T)=x'(0)-x'(T)=0,\) where the Carathéodory function g: [0,T]\(\times {\mathbb{R}}\to {\mathbb{R}}\) grows at most linearly. There are proved existence results when the nonlinearity g is at resonance with two successive eigenvalues of the associated linear operator and satisfies some Landesman-Lazer type conditions.