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Multiplicity and concentration results for a fractional Choquard equation via penalization method (1712.01124v1)
Published 1 Dec 2017 in math.AP
Abstract: This paper is devoted to the study of the following fractional Choquard equation $$ \varepsilon{2s}(-\Delta){s} u + V(x)u = \varepsilon{\mu-N}\left(\frac{1}{|x|{\mu}}*F(u)\right)f(u) \mbox{ in } \mathbb{R}{N}, $$ where $\varepsilon>0$ is a parameter, $s\in (0, 1)$, $N>2s$, $(-\Delta){s}$ is the fractional Laplacian, $V$ is a positive continuous potential with local minimum, $0<\mu<2s$, 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.