In this article, we are interested in multi-bump solutions of the singularly perturbed problem -ε2⁢Δ⁢v+V⁢(x)⁢v=f⁢(v) in ⁢ℝN.-\varepsilon^{2}\Delta v+V(x)v=f(v)\quad\text{in }\mathbb{R}^{N}. Extending previous results, we prove the existence of multi-bump solutions for an optimal class of nonlinearities f satisfying the Berestycki–Lions conditions and, notably, also for more general classes of potential wells than those previously studied. We devise two novel topological arguments to deal with general classes of potential wells. Our results prove the existence of multi-bump solutions in which the centers of bumps converge toward potential wells as ε→0{\varepsilon\rightarrow 0}. Examples of potential wells include the following: the union of two compact smooth submanifolds of ℝN{\mathbb{R}^{N}} where these two submanifolds meet at the origin and an embedded topological submanifold of ℝN{\mathbb{R}^{N}}.

中文翻译：

---

具有一般非线性的非线性Schrödinger方程的多凸点驻波：势阱的拓扑效应

在本文中，我们对⁢ℝN中的奇摄动问题-ε2⁢Δ⁢v+V⁢（x）⁢v=f⁢（v）的多凸点解感兴趣。-\ varepsilon ^ {2} \ Delta v + V（x）v = f（v）\ quad \ text {in} \ mathbb {R} ^ {N}。扩展先前的结果，我们证明了对于满足Berestycki–Lions条件的最优非线性f类，尤其是对于比以前研究的潜在井更通用的类，存在多重碰撞解决方案。我们设计了两种新颖的拓扑论证来处理潜在井的一般类别。我们的结果证明了多凸点解决方案的存在，其中凸点的中心向势阱收敛，如ε→0 {\ varepsilon \ rightarrow 0}。潜在井的示例包括：