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arXiv · 1609.03793

On a class of mixed Choquard-Schrödinger-Poisson system

Marius Ghergu·Gurpreet Singh
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Abstract

We study the system $$ \left\{ -Δu+u+K(x) ϕ|u|^{q-2}u&=(I_α*|u|^p)|u|^{p-2}u &&\mbox{ in }{\mathbb R}^N, -Δϕ&=K(x)|u|^q&&\mbox{ in }{\mathbb R}^N, \right. $$ where $N\geq 3$, $α\in (0,N)$, $p,q>1$ and $K\geq 0$. Using a Pohozaev type identity we first derive conditions in terms of $p,q,N,α$ and $K$ for which no solutions exist. Next, we discuss the existence of a ground state solution by using a variational approach.

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Marius Ghergu, Gurpreet Singh. 2017-03-07. On a class of mixed Choquard-Schrödinger-Poisson system. https://arxiv.org/abs/1609.03793

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