Using variational arguments the authors prove the existence of a weak solution for the boundary value problem
where div, , is a bounded domain of , and is a bounded Carathéodory function such that there exist a.e. in , with either
for all Ker, and also there is such that
The conditions (LL) are the standard Landesman – Laser conditions for resonance problems, and of course are trivially satisfied whenever is not an eigenvalue.