Calculus of Variations and Geometric Measure Theory
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X. He - M. Squassina - W. Zou

The Nehari manifold for fractional systems involving critical nonlinearities

created by squassina on 09 Sep 2015



Inserted: 9 sep 2015
Last Updated: 9 sep 2015

Pages: 23
Year: 2015


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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