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arXiv · 1712.01124

Multiplicity and concentration results for a fractional Choquard equation via penalization method

Vincenzo Ambrosio
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Abstract

This paper is devoted to the study of the following fractional Choquard equation $$ \varepsilon^{2s}(-Δ)^{s} u + V(x)u = \varepsilon^{μ-N}\left(\frac{1}{|x|^μ}*F(u)\right)f(u) \mbox{ in } \mathbb{R}^{N}, $$ where $\varepsilon>0$ is a parameter, $s\in (0, 1)$, $N>2s$, $(-Δ)^{s}$ is the fractional Laplacian, $V$ is a positive continuous potential with local minimum, $0<μ<2s$, and $f$ is a superlinear continuous function with subcritical growth. By using the penalization method and the Ljusternik-Schnirelmann theory, we investigate the multiplicity and concentration of positive solutions for the above problem.

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Vincenzo Ambrosio. 2017-12-01. Multiplicity and concentration results for a fractional Choquard equation via penalization method. https://doi.org/10.1007/s11118-017-9673-3

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