The Nehari manifold for fractional systems involving critical nonlinearities

Xiaoming He; Marco Squassina; Wenming Zou

The Nehari manifold for fractional systems involving critical nonlinearities

Analysis of PDEs 2016-01-12 v4

Authors: Xiaoming He , Marco Squassina , Wenming Zou

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 $\R^2$ .

Keywords

fractional systems critical nonlinearities Nehari manifold positive solutions Sobolev exponents concave-convex nonlinearities

Cite

@article{arxiv.1509.02713,
  title  = {The Nehari manifold for fractional systems involving critical nonlinearities},
  author = {Xiaoming He and Marco Squassina and Wenming Zou},
  journal= {arXiv preprint arXiv:1509.02713},
  year   = {2016}
}

Comments

To appear in Commun. Pure Applied Anal

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