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

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.

arXiv comment16 pages. arXiv admin note: text overlap with arXiv:1411.2198

References in corpus (6)

• Local behavior of fractional $p$-minimizers
• Fractional p-eigenvalues
• On fractional p-Laplacian problems with weight
• Bifurcation and multiplicity results for critical fractional p-Laplacian problems
• Positive solutions to some asymptotically linear fractional Schrodinger equations
• On a class of critical $(p,q)$-Laplacian problems