一类反应扩散方程的Nehari-Pankov型基态解

数学物理学报 ›› 2021, Vol. 41 ›› Issue (5): 1347-1356.

一类反应扩散方程的Nehari-Pankov型基态解

陈鹏()

^{三峡大学理学院 & 三峡大学数学研究中心湖北宜昌 443002}

收稿日期:2021-01-18 出版日期:2021-10-26 发布日期:2021-10-08
作者简介:陈鹏, E-mail: pengchen729@sina.com
基金资助:
湖北省教育厅重点项目(D20161206)

Ground State Solutions of Nehari-Pohozaev Type for a Class of Reaction-Diffusion System

Peng Chen()

^{College of Science & Three Gorges Mathematical Research Center, China Three Gorges University, Hubei Yichang 443002}

Received:2021-01-18 Online:2021-10-26 Published:2021-10-08
Supported by:
the Key Projects of Hubei Provincial Department of Education(D20161206)

摘要/Abstract

摘要：

该文考虑了一类非线性反应扩散系统，利用强不定泛函理论中Non-Nehari流形方法，当非线性项满足超线性增长条件时，给出了一个更直接、简便的证明基态解的方法.在没有严格单调条件的情况下，证明了Nehari-Pankov型基态解的存在性，获得了这方面新的结果.

关键词: 基态解, 反应扩散系统, Non-Nehari流形方法

Abstract:

In this paper, we consider a class of nonlinear reaction diffusion systems, by using the non Nehari manifold method in strongly indefinite functional theory, a more direct and simple method to prove the ground state solution is given when the nonlinear term is superlinear. The existence of Nehari pankov type ground state solution is proved without strict monotone condition, and some new results are obtained.

Key words: Reaction-diffusion system, Ground states, Strongly indefinite functional

中图分类号:

O175.25

陈鹏. 一类反应扩散方程的Nehari-Pankov型基态解[J]. 数学物理学报, 2021, 41(5): 1347-1356.

Peng Chen. Ground State Solutions of Nehari-Pohozaev Type for a Class of Reaction-Diffusion System[J]. Acta mathematica scientia,Series A, 2021, 41(5): 1347-1356.

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