一类p-Laplace方程基态解的存在性
Existence of Ground State Solutions for a Class of p-Laplace Equations
DOI: 10.12677/AAM.2023.121044, PDF, HTML,    国家自然科学基金支持
作者: 刘文静, 许丽萍*：河南科技大学数学与统计学院，河南洛阳
关键词: p-Laplace方程；Pohozaev恒等式；变分法；基态解；p-Laplace Equations； Pohozaev Equality； Variational Methods； Ground State Solutions
摘要: 文章研究了如下形式的p-Laplace方程： 其中 , 常数V>0。当非线性项/在无穷远处满足超线性但不满足通常的 Ambrosetti-Rabinowitz (简称AR)条件时，通过运用新的技巧，借助Pohozaev恒等式, 获得了上述方程基态解的存在性，所得结果推广了相关文献的研究成果。
Abstract: In this paper, we study the following p-Laplace type equation: where and V > 0 is constant. By introducing some new tricks and Pohozaev equality, when the nonlinear function / satisfies the superlinear condition at infinity, the existence of ground state solution of this equation is obtained without assuming Ambrosetti - Rabinowitz type condition. Our results generalize the research results of related literatures.
文章引用：刘文静, 许丽萍. 一类p-Laplace方程基态解的存在性[J]. 应用数学进展, 2023, 12(1): 411-427. https://doi.org/10.12677/AAM.2023.121044

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