The Nehari manifold for fractional systems involving critical nonlinearities

Xiaoming He; Marco Squassina; Wenming Zou

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arXiv · 1509.02713

The Nehari manifold for fractional systems involving critical nonlinearities

Xiaoming He·Marco Squassina·Wenming Zou

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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 $\R^2$.

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Xiaoming He, Marco Squassina, Wenming Zou. 2015-09-09. The Nehari manifold for fractional systems involving critical nonlinearities. https://arxiv.org/abs/1509.02713

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