Sull'esistenza di autovalori per un problema al contorno non lineare

In this paper the existence of infinitely many eigenvalues for the non linear boundary value problem {Mathematical expression} Ωt Rn bounded and {Mathematical expression} (λ1, λ2)where λ1and λ2are the first and the second eigenvalue of - Δ respectively. The eigenvalues are characterized by the critical levels of a suitable functional on a smooth unbounded manifold. The usual method is not applicable because the functional is not positive definite and the Palais-Smale condition is not satisfied. We applies a technique introduced in a preceding paper [3]