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arXiv · 1305.2031

An existence result for a class of quasilinear elliptic eigenvalue problems in unbounded domains

Kanishka Perera·Patrizia Pucci·Csaba Varga
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Abstract

We consider a nonlinear eigenvalue problem under Robin boundary conditions in a domain with (possibly noncompact) smooth boundary. The problem involves a weighted p-Laplacian operator and subcritical nonlinearities satisfying Ambrosetti-Rabinowitz type conditions. Using Morse theory and a cohomological local splitting as in Degiovanni et al. [5], we prove the existence of a nontrivial weak solution for all (real) values of the eigenvalue parameter. Our result is new even in the semilinear case p = 2 and complements some recent results obtained in Autuori et al. [1].

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Kanishka Perera, Patrizia Pucci, Csaba Varga. 2013-05-09. An existence result for a class of quasilinear elliptic eigenvalue problems in unbounded domains. https://arxiv.org/abs/1305.2031

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