具有Choquard项的拟线性Schrodinger-Poisson系统的非平凡解
Nontrivial Solutions of Quasilinear Schrodinger-Poisson Systems with Choquard Terms
DOI: 10.12677/PM.2022.122034, PDF, HTML, 下载: 450  浏览: 651  国家自然科学基金支持
作者: 平 锐, 廖 鹏, 陈绍雄*：云南师范大学数学学院，云南 昆明
关键词: 拟线性薛定号方程；变分法；非平凡解；Quaslinear Schr?dinger Equation； Variational Argument； Nontrivial Solution
摘要: 本文研究具有Choquard项的拟线性Schrodinger-Poisson 系统的非平凡解 其中α∈(0,3),4+α≤p < 6+α,V∈C(ℝ3,ℝ)，并且Iα:ℝ33→ℝ是里斯位势。在V(x)的某些假设下，我们利用变分法与变量替换证明非平凡解的存在性。
Abstract: In this paper, we study the existence of nontrivial solutions for a class of quasilinear Schrödinger equations of Choquard type: where α∈(0,3),4+α≤p < 6+2α,V∈C(ℝ3, ℝ) and Iα: ℝ33→ℝ is the Riesz potential. Under some assumptions on V(x), we establish the existence of nontrivial solutions. Under the above assumptions, we use variational argument and variable substitution to prove the existence of nontrivial solution.
文章引用：平锐, 廖鹏, 陈绍雄. 具有Choquard项的拟线性Schrodinger-Poisson系统的非平凡解[J]. 理论数学, 2022, 12(2): 287-308. https://doi.org/10.12677/PM.2022.122034

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