Summary
In this paper the existence of infinitely many eigenvalues for the non linear boundary value problem
ΩtR n bounded and\(\bar \lambda \in \) (λ1, λ2)where λ1 and λ2 are 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].
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Cerami, G. Sull'esistenza di autovalori per un problema al contorno non lineare. Annali di Matematica pura ed applicata 124, 161–179 (1980). https://doi.org/10.1007/BF01795391
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DOI: https://doi.org/10.1007/BF01795391