The Nehari manifold for fractional systems involving critical nonlinearities. (English) Zbl 06636876
Summary: 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 \(\mathbb R^2\).
MSC:
| 47G20 | Integro-differential operators |
| 35J50 | Variational methods for elliptic systems |
| 35B65 | Smoothness and regularity of solutions to PDEs |
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