Abstract
This paper is concerned with a fractional [Formula: see text]-Laplacian system with both concave–convex nonlinearities. The existence and multiplicity results of positive solutions are obtained by variational methods and the Nehari manifold.
Highlights
We study the existence of nontrivial solutions to the following fractional p-Laplacian involving combined critical nonlinearities:
(− )spU = S∗U p∗s −1, in RN, where Ds,p(RN ) is the fractional Beppo–Levi space, that is the completion of C0∞(RN ) with respect to [·]s,p
We present some properties of Nη+,ν, Nη0,ν and Nη−,ν to state our main result
Summary
This paper is concerned with a fractional p-Laplacian system with both concave–convex nonlinearities. The existence and multiplicity results of positive solutions are obtained by variational methods and the Nehari manifold. This is an Open Access article published by World Scientific Publishing Company.
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