# The Nehari manifold for fractional systems involving critical nonlinearities

created by squassina on 09 Sep 2015

[BibTeX]

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 ${\mathbb R}^2$.