含变号位势的p-Kirchhoff型方程组无穷多个高能量解的存在性

数学物理学报 ›› 2017, Vol. 37 ›› Issue (5): 869-876.

含变号位势的p-Kirchhoff型方程组无穷多个高能量解的存在性

李琴¹, 杨作东^2,3

1. 安徽财经大学统计与应用数学学院安徽蚌埠 233030;
2. 南京师范大学教师教育学院南京 210097;
3. 南京师范大学数学科学学院南京 210023

收稿日期:2016-12-07 修回日期:2017-05-24 出版日期:2017-10-26 发布日期:2017-10-26
作者简介:李琴,E-mail:liqin-math@163.com;杨作东,E-mail:zdyang-jin@263.net
基金资助:
国家自然科学基金（11571093，11471164）和安徽高校自然科学研究项目（KJ2017A432）

Infinitely Many High Energy Solutions of p-Kirchhoff-Type System with Sign-Changing Weight

Li Qin¹, Yang Zuodong^2,3

1. School of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Anhui Bengbu 233030;
2. School of Teacher Education, Nanjing Normal University, Nanjing 210097;
3. School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023

Received:2016-12-07 Revised:2017-05-24 Online:2017-10-26 Published:2017-10-26
Supported by:
Supported by the NSFC (11571093, 11471164) and the Natural Science Foundation of Education Bureau of Anhui Province (KJ2017A432)

摘要/Abstract

摘要： 该文主要研究一类含变号位势的p-Kirchhoff型方程组，利用对称山路引理，证明了无穷多个高能量解的存在性，推广并完善了文献[3-4，6]中的相关结果.

关键词: 存在性, 无穷多解, 对称山路引理, 变号位势

Abstract: In this paper, we study a p-Kirchhoff-type system with sign-changing weight. Under some more general assumptions, we obtain the existence of infinitely many high energy solutions by using the Symmetric Mountain Pass Theorem of Rabinowitz^{[10, Theorem 9.12]}, which unifies and generalizes the recent results of Zhou et al^[3], Wu^[4] and Li et al^[6].

Key words: Existence, Infinitely many solutions, Symmetric Mountain Pass Theorem, Signchanging weight

中图分类号:

O175.2

李琴, 杨作东. 含变号位势的p-Kirchhoff型方程组无穷多个高能量解的存在性[J]. 数学物理学报, 2017, 37(5): 869-876.

Li Qin, Yang Zuodong. Infinitely Many High Energy Solutions of p-Kirchhoff-Type System with Sign-Changing Weight[J]. Acta mathematica scientia,Series A, 2017, 37(5): 869-876.

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