In this article, we study the existence and asymptotic behavior of multi-bump solutions for nonlinear Choquard equation with a general nonlinearity \begin{equation*} -\Delta u+(\lambda a(x)+1)u=\Big(\frac{1}{|x|^{\alpha}}\ast F(u)\Big)f(u) \ \ \text{in}\ \ \mathbb{R}^{N}, \end{equation*} where $N\geq 3$, $0<\alpha< \min\{N,4\}$, $\lambda$ is a positive parameter and the nonnegative potential function $a(x)$ is continuous. Using variational methods, we prove that if the potential well int$(a^{-1}(0))$ consists of $k$ disjoint components, then there exist at least $2^k-1$ multi-bump solutions. The asymptotic behavior of these solutions is also analyzed as $\lambda\to +\infty$.
Lun GUO
,
Tingxi HU
. MULTI-BUMP SOLUTIONS FOR NONLINEAR CHOQUARD EQUATION WITH POTENTIAL WELLS AND A GENERAL NONLINEARITY[J]. Acta mathematica scientia, Series B, 2020
, 40(2)
: 316
-340
.
DOI: 10.1007/s10473-020-0202-x
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