论文标题
具有一般非线性的非线性Schrodinger方程的多重凹凸式站波：潜在井的拓扑作用
Multi-bump standing waves for nonlinear Schrodinger equations with a general nonlinearity: the topological effect of potential wells
论文作者
论文摘要
在本文中，我们对奇异扰动的问题的多重倾斜解决方案感兴趣\ begin {qore*}-ε^2ΔV+v（x）v = f（v）\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ r^n。 \ end {equation*}扩展了先前的结果\ cite {b，dly，w1}，我们证明了为最佳类别的非线性类别$ f $ $ f $提供的多重倾斜解决方案的存在，并且值得注意的是，对于那些先前研究的潜在井也是如此的一般性级别。我们设计了两个新颖的拓扑论点来处理一般的潜在井类。我们的研究结果证明了多重倾斜解决方案的存在，在这种解决方案中，颠簸中心以$ε\ rightarrow 0 $汇聚为潜在的井。潜在井的示例包括以下内容：两个紧凑的平滑子手机的结合$ \ r^n $，这两个子曼属在原点与$ \ r^n $相遇。
In this article, we are interested in multi-bump solutions of the singularly perturbed problem \begin{equation*} -ε^2Δv+V(x)v=f(v) \ \ \mbox{ in }\ \ \R^N. \end{equation*} Extending previous results \cite{B, DLY,W1}, 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 $ε\rightarrow 0$. Examples of potential wells include the following: the union of two compact smooth submanifolds of $\R^N$ where these two submanifolds meet at the origin and an embedded topological submanifold of $\R^N$.
