Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6415001 | Journal of Functional Analysis | 2016 | 29 Pages |
Abstract
We consider the general Choquard equationsâÎu+u=(Iαâ|u|p)|u|pâ2u where Iα is a Riesz potential. We construct minimal action odd solutions for pâ(N+αN,N+αNâ2) and minimal action nodal solutions for pâ(2,N+αNâ2). We introduce a new minimax principle for least action nodal solutions and we develop new concentration-compactness lemmas for sign-changing Palais-Smale sequences. The nonlinear Schrödinger equation, which is the nonlocal counterpart of the Choquard equation, does not have such solutions.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Marco Ghimenti, Jean Van Schaftingen,