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 Z2-cohomological index
Perera, K., Squassina, M., Yang, Y., Critical fractional p-Laplacian problems with possibly vanishing potentials, <<JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS>>, 2016; 433 (N/A): 818-831. [doi:10.1016/j.jmaa.2015.08.024] [http://hdl.handle.net/10807/87033]
Critical fractional p-Laplacian problems with possibly vanishing potentials
Squassina, MarcoSecondo
;
2016
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 Z2-cohomological index
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