一类带有临界增长的广义拟线性SchrO¨dinger-Poisson系统基态变号解的存在性
Existence of the Ground State Sign-Changing Solution for a Class of Generalized Quasilinear SchrO¨dinger-Poisson System
摘要: 在这篇文章当中，我们研究了如下Schrödinger-Poisson系统其中是边界光滑的有界区域，。对f,g施加适当的条件，若μ足够大，通过利用约束变分方法和形变引理，得到了该系统对于每一个λ>0都有相对应的基态变号解νλ，并且基态变号解的能量严格大于二倍基态解的能量。
Abstract: In this paper, we study the following Schrödinger-Poisson system where is a bounded domain with a smooth boundary , , under suitable conditions of f,g, by using constraint variational method and the quantitative deformation lemma, if μ is large enough, we obtain a ground state sign-changing solution νλ to this problem for each λ>0, and its energy is strictly large than twice that of the ground state solutions.
文章引用：褚海慧. 一类带有临界增长的广义拟线性SchrO¨dinger-Poisson系统基态变号解的存在性[J]. 应用数学进展, 2021, 10(6): 2137-2150. https://doi.org/10.12677/AAM.2021.106223

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