We consider the general Choquard equations-δu+u=(Iα*|u|p)|u|p-2u where Iα is a Riesz potential. We construct minimal action odd solutions for p∈(N+α/N,N+α/N-2) and minimal action nodal solutions for p∈(2,N+α/N-2). 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.
Nodal solutions for the Choquard equation
GHIMENTI, MARCO GIPO;
2016-01-01
Abstract
We consider the general Choquard equations-δu+u=(Iα*|u|p)|u|p-2u where Iα is a Riesz potential. We construct minimal action odd solutions for p∈(N+α/N,N+α/N-2) and minimal action nodal solutions for p∈(2,N+α/N-2). 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.File in questo prodotto:
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