The Nehari manifold for fractional systems involving critical nonlinearities

By Xiaoming He, Marco Squassina, Wenming Zou. 2015

71 citations recorded by the source corpus.

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 $\R^2$.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/22d5d104e3aa264aa56931fd6df5ee8c84496e1d

How researchers see this paper

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In Applied Mathematics

1. Wenjing Chen
2. Marco Squassina
3. Patrick Winkert
4. Binlin Zhang
5. Vicentiu D. Rădulescu

In Computational Theory and Mathematics

1. Wenjing Chen
2. Marco Squassina
3. Patrick Winkert
4. Binlin Zhang
5. Vicentiu D. Rădulescu

Citations in the corpus

• Critical Nonlocal Systems with Concave-Convex Powers (2016, background): “For the fractional system with p = 2, we mention [10, 13].”