Abstract
In present paper, we study the fractional Choquard equation $$\varepsilon^{2s}(-\Delta)^s u+V(x)u=\varepsilon^{\mu-N}(\frac{1}{|x|^\mu}\ast F(u))f(u)+|u|^{2^\ast_s-2}u$$ where $\varepsilon>0$ is a parameter, $s\in(0,1),$ $N>2s,$ $2^*_s=\frac{2N}{N-2s}$ and $0<\mu<\min\{2s,N-2s\}$. Under suitable assumption on $V$ and $f$, we prove this problem has a nontrivial nonnegative ground state solution. Moreover, we relate the number of nontrivial nonnegative solutions with the topology of the set where the potential attains its minimum values and their's concentration behavior.
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More From: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
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