Annali di Matematica Pura ed Applicata

, Volume 124, Issue 1, pp 161–179 | Cite as

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

  • Giovanna Cerami


In this paper the existence of infinitely many eigenvalues for the non linear boundary value problem
$$\left\{ \begin{gathered} - \Delta u - \bar \lambda u = \mu \alpha (u) \hfill \\ u|_{\partial \Omega } = 0 \hfill \\ \end{gathered} \right.$$
ΩtRn bounded and\(\bar \lambda \in \)1, 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].


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Copyright information

© Nicola Zanichelli Editore 1980

Authors and Affiliations

  • Giovanna Cerami
    • 1
  1. 1.Palermo

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