分数阶Kirchhoff-SchrÖdinger-Poisson系统解的存在性

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分数阶Kirchhoff-SchrÖdinger-Poisson系统解的存在性
Existence of Nontrivial Solution for a Class of Fractional Kirchhoff-SchrÖdinger-Poisson System

DOI: 10.12677/AAM.2024.135208, PDF, 下载: 29 浏览: 58
作者: 张召翔：兰州理工大学，理学院，甘肃兰州
关键词: 分数阶Kirchhoff-SchrÖdinger-Poisson系统；变号权；变分法；Fractional Kirchhoff-SchrÖdinger-Poisson System； Sign-Changing Weight； Variation Methods

摘要: 本文研究如下分数阶Kirchhoff-SchrÖdinger-Poisson系统

, 非平凡解的存在性, 其中 a, b > 0 ,

, s, t ∈ (0, 1) 且 4s + 2t > 3, W (x) ∈ C(R³) 变号且 lim_|x|→∞ W (x) = W_∞ < 0 ,

. 应用山路引理, 本文得到该系统至少存在一个非平凡解.

Abstract: In this paper, we study the existence of nontrivial solution for fractional Kirchhoff- SchrÖdinger-Poisson system:

, where a, b > 0,

, s, t ∈ (0, 1) and 4s + 2t > 3, W (x) ∈ C(R³) is a sign-changing function with lim_|x|→∞ W (x) = W_∞ < 0,

. By using mountain pass lemma, we obtain that this system has at least one nontrivial solution.

文章引用：张召翔. 分数阶Kirchhoff-SchrÖdinger-Poisson系统解的存在性[J]. 应用数学进展, 2024, 13(5): 2191-2198. https://doi.org/10.12677/AAM.2024.135208

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