Choquard Equations with Mixed Potential

2015/06/26 by Souto, Marco A. S., de Lima, Romildo N.
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1506.08179

Abstract

In this paper, we study the following class of nonlinear Choquard equation, -Δu+a(z)u=K(u)f(u) in \R^N, where \R^N=\R^L×\R^M, L≥2, K(u)=|.|^-γ*F(u), γ∈(0,N), a is a continuous real function and F is the primitive function of f. Under some suitable assumptions mixed on the potential a. We prove existence of a nontrivial solution for the above equation.

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