Abstract
In this article, we study the existence and asymptotic behavior of multi-bump solutions for nonlinear Choquard equation with a general nonlinearity $$-\Delta u + (\lambda a(x) + 1)u = \left(\frac{1}{|x|^\alpha}* F(u)\right) f(u) \; in \; \mathbb{R}^N,$$ where N ≥ 3, 0 < α < min{N, 4}, λ 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 2k − 1 multi-bump solutions. The asymptotic behavior of these solutions is also analyzed as λ → +∞.
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