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arXiv · 1504.01533

Critical fractional $p$-Laplacian problems with possibly vanishing potentials

Kanishka Perera·Marco Squassina·Yang Yang
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Abstract

We obtain nontrivial solutions of a critical fractional $p$-Laplacian equation in the whole space and with possibly vanishing potentials. In addition to the usual difficulty of the lack of compactness associated with problems involving critical Sobolev exponents, the problem is further complicated by the absence of a direct sum decomposition suitable for applying classical linking arguments. We overcome this difficulty using a generalized linking construction based on the ${\mathbb Z}_2$-cohomological index.

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Kanishka Perera, Marco Squassina, Yang Yang. 2015-04-07. Critical fractional $p$-Laplacian problems with possibly vanishing potentials. https://arxiv.org/abs/1504.01533

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