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 2^k − 1 multi-bump solutions. The asymptotic behavior of these solutions is also analyzed as λ → +∞.

中文翻译：

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具有潜在势阱和一般非线性项的非线性Choquard方程的多凸点解

在本文中，我们研究具有一般非线性$$-\ Delta u +（\ lambda a（x）+ 1）u = \ left（\ frac {1}的非线性Choquard方程的多凸点解的存在性和渐近行为} {| x | ^ \ alpha} * F（u）\ right）f（u）\; 在\;中 \ mathbb {R} ^ N，$$其中N≥3，0 < α <min { N，4}，λ是一个正参数，非负电势函数a（x）是连续的。使用变分方法，我们证明了如果势阱int（a ^-1（0））由k个不相交的分量组成，那么至少存在2 ^k -1个多峰解决方案。这些解的渐近行为也被分析为λ→+∞。