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

作者: 王 星 :云南师范大学数学学院,云南 昆明;

关键词: 半经典 SchrO">¨dinger-Poisson 方程组下降流不变集方法截断技巧无穷多变号解集中现象Semiclassical SchrO">¨dinger-Poisson System Infinitely Many Sign-Changing Solutions The Method of Invariant Sets with Descending Flow The Truncation Technique Infinitely Many Sign-Changing Solutions Concentration

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 : 3 → 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 (2021) 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。 应用数学进展, 10, 1359-1379. doi: 10.12677/AAM.2021.104146

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