Min-max levels transition in parametrized elliptic problems on unbounded domains

  • Giuseppe Devillanova

    Politecnico di Bari, Italy
  • Sergio Solimini

    Politecnico di Bari, Italy
Min-max levels transition in parametrized elliptic problems on unbounded domains cover
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Abstract

We discuss some attempts to apply the classical variational methods, in the spirit of Ambrosetti–Rabinowitz, to parametrized elliptic problems defined on unbounded domains. We construct some min-max classes and establish some estimates which allow, for instance, to conclude that, while for a generic coefficient there is always a solution for all small values of the parameter, in the case of a coefficient with a suitable exponential decay and in dimension the set of the values of the parameter for which the problem has a nontrivial solution is unbounded.

Cite this article

Giuseppe Devillanova, Sergio Solimini, Min-max levels transition in parametrized elliptic problems on unbounded domains. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 33 (2022), no. 3, pp. 677–694

DOI 10.4171/RLM/985