On the multiplicity and concentration of positive solutions for a $p$-fractional Choquard equation in $\mathbb{R}^{N}$

Vincenzo Ambrosio

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arXiv · 1810.03171

On the multiplicity and concentration of positive solutions for a $p$-fractional Choquard equation in $\mathbb{R}^{N}$

Vincenzo Ambrosio

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Abstract

In this paper we deal with the following fractional Choquard equation \begin{equation*} \left\{ \begin{array}{ll} \varepsilon^{sp}(-Δ)^{s}_{p} u + V(x)|u|^{p-2}u = \varepsilon^{μ-N}\left(\frac{1}{|x|^μ}*F(u)\right)f(u) \mbox{ in } \mathbb{R}^{N},\\ u\in W^{s,p}(\R^{N}), \quad u>0 \mbox{ in } \mathbb{R}^{N}, \end{array} \right. \end{equation*} where $\varepsilon>0$ is a small parameter, $s\in (0, 1)$, $p\in (1, \infty)$, $N>sp$, $(-Δ)^{s}_{p}$ is the fractional $p$-Laplacian, $V$ is a positive continuous potential, $0<μ 0$ small enough.

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Vincenzo Ambrosio. 2019-05-11. On the multiplicity and concentration of positive solutions for a $p$-fractional Choquard equation in $\mathbb{R}^{N}$. https://arxiv.org/abs/1810.03171

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