Critical Nonlocal Systems with Concave-Convex Powers

By Wenjing Chen, Marco Squassina. 2016

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Abstract By using the fibering method jointly with Nehari manifold techniques, we obtain the existence of multiple solutions to a fractional p-Laplacian system involving critical concave-convex nonlinearities, provided that a suitable smallness condition on the parameters involved is assumed. The result is obtained although there is no general classification for the optimizers of the critical fractional Sobolev embedding.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/665a43b9f28757237d3de38310d9a8d175c5b68f