We prove the existence of a minimal action nodal solution for the quadratic Choquard equation (Formula presented), where Iα is the Riesz potential of order α ∈ (0,N). The solution is constructed as the limit of minimal action nodal solutions for the nonlinear Choquard equations (Formula presented) when p (symbol found) 2. The existence of minimal action nodal solutions for p > 2 can be proved using a variational minimax procedure over a Nehari nodal set. No minimal action nodal solutions exist when p < 2.

Least action nodal solutions for the quadratic choquard equation

GHIMENTI, MARCO GIPO;
2017-01-01

Abstract

We prove the existence of a minimal action nodal solution for the quadratic Choquard equation (Formula presented), where Iα is the Riesz potential of order α ∈ (0,N). The solution is constructed as the limit of minimal action nodal solutions for the nonlinear Choquard equations (Formula presented) when p (symbol found) 2. The existence of minimal action nodal solutions for p > 2 can be proved using a variational minimax procedure over a Nehari nodal set. No minimal action nodal solutions exist when p < 2.
2017
Ghimenti, MARCO GIPO; Moroz, Vitaly; Van Schaftingen, Jean
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/850659
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