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 (λ, µ) belongs to a suitable subset of R^2
He, X., Squassina, M., Zou, W., The Nehari manifold for fractional systems involving critical nonlinearities, <<COMMUNICATIONS ON PURE AND APPLIED ANALYSIS>>, 2016; 15 (N/A): 1285-1308. [doi:10.3934/cpaa.2016.15.1285] [http://hdl.handle.net/10807/87016]
The Nehari manifold for fractional systems involving critical nonlinearities
Squassina, Marco;
2016
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 (λ, µ) belongs to a suitable subset of R^2
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