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arXiv · 1410.2984

On a class of critical $(p,q)$-Laplacian problems

Pasquale Candito·Salvatore A. Marano·Kanishka Perera
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Abstract

We obtain nontrivial solutions of a critical $(p,q)$-Laplacian problem in a bounded domain. In addition to the usual difficulty of the loss of compactness associated with problems involving critical Sobolev exponents, this problem lacks a direct sum decomposition suitable for applying the classical linking theorem. We show that every Palais-Smale sequence at a level below a certain energy threshold admits a subsequence that converges weakly to a nontrivial critical point of the variational functional. Then we prove an abstract critical point theorem based on a cohomological index and use it to construct a minimax level below this threshold.

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Pasquale Candito, Salvatore A. Marano, Kanishka Perera. 2014-10-11. On a class of critical $(p,q)$-Laplacian problems. https://arxiv.org/abs/1410.2984

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