半经典次临界增长SchrO¨dinger-Poisson方程组变号解的存在性和集中现象
Existence and Concentration of Infinitely Many Sign-Changing Solutions of Semiclassical Subcritical GrowthSchrO¨dinger-Poisson Systems
摘要: 在本文中，研究半经典次临界增长 Schrödinger-Poisson 方程组, 当 |x| → ∞ 时, 其中 ε > 0 是小参数，λ, µ > 0 是参数，V : ℝ3 → ℝ 是有界位势函数且局部极小点集 M 非空， 利用下降流不变集方法和截断技巧证明无穷多变号解的存在性，当 ε → 0 时，通过构造惩罚项证明这些解集中在位势函数 V 的局部极小附近。
Abstract: In this paper, we study the following semiclassical Schrödinger-Poisson system , where ε > 0 is a small parameter, λ > 0 is a parameter and V : ℝ3 → ℝ is a bounded potential function, the nonlinearity f is superlinear at the origin and at infinity, and is subcritical growth. We proved the existence of infinitely many sign-changing solutions by the method of invariant sets with descending flow and the truncation technique, and proved that these solutions are located near the local minimum point of the potential function V as ε → 0 by the penalization method.
文章引用：王星. 半经典次临界增长SchrO¨dinger-Poisson方程组变号解的存在性和集中现象[J]. 应用数学进展, 2021, 10(4): 1359-1379. https://doi.org/10.12677/AAM.2021.104146

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