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arXiv · 1506.08179

Choquard Equations with Mixed Potential

Marco A. S. Souto·Romildo N. de Lima
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Abstract

In this paper, we study the following class of nonlinear Choquard equation, $$-\Delta u+a(z)u=K(u)f(u)\quad \text{in}\quad \R^N,$$ where $\R^N=\R^L\times\R^M$, $L\geq2$, $K(u)=|.|^{-\gamma}*F(u)$, $\gamma\in(0,N)$, $a$ 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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Marco A. S. Souto, Romildo N. de Lima. 2015-06-26. Choquard Equations with Mixed Potential. https://arxiv.org/abs/1506.08179

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