Preprint

Inserted: 9 sep 2015
Last Updated: 9 sep 2015

Pages: 23
Year: 2015

Abstract:

We study the combined effect of concave and convex nonlinearities on the number of positive solutions for a fractional system involving critical Sobolev exponents. With the help of the Nehari manifold, we prove that the system admits at least two positive solutions when the pair of parameters $(\lambda,\mu)$ belongs to a suitable subset of ${\mathbb R}^2$.

Keywords: Fractional elliptic systems, Nehari manifold, Concave-convex nonlinearities

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• He-Squassina-Zou-15.pdf