含指数增长非线性项的椭圆方程的多解性

doi:10.3969/j.issn.0253-2778.2020.03.007

中国科学技术大学学报 ›› 2020, Vol. 50 ›› Issue (3): 300-311.DOI: 10.3969/j.issn.0253-2778.2020.03.007

含指数增长非线性项的椭圆方程的多解性

薛益民，陈守婷

徐州工程学院数学与物理科学学院,江苏徐州 221018

收稿日期:2019-03-23 修回日期:2019-06-14 接受日期:2019-06-14 出版日期:2020-03-31 发布日期:2019-06-14

Multiplicity of solutions to elliptic equations with exponential nonlinearities

XUE Yimin, CHEN Shouting

Received:2019-03-23 Revised:2019-06-14 Accepted:2019-06-14 Online:2020-03-31 Published:2019-06-14
Contact: XUE Yimin
About author:XUE Yimin(corresponding author), male, born in 1977, master/lecturer. Research field: Differential equations and their applications. E-mail: xueym@xzit.edu.cn
Supported by:
The Natural Science Foundation of NNSF funds of NNSF of China (11526177), the Natural Science Foundation of Jiangsu Province (BK20151160), the Nurturing Project of Xuzhou University of Technology (XKY2019103).

摘要/Abstract

摘要： 利用Li的一个奇异Trudinger-Moser不等式、没有Palais-Smale条件的山路引理和Ekeland 的变分原理, 借鉴文献[11,15]的方法证明了一类含指数增长非线性项的椭圆形方程的多解性.

关键词: 奇异Trudinger-Moser不等式, 山路引理, 指数增长, 多解

Abstract: The multiplicity of positive solutions to quasi-linear elliptic equations with exponential nonlinearities is obtained through a singular Trudinger-Moser inequality, which is due to Ref.[21], the mountain-pass theorem without the Palais-Smale condition and the Ekeland’s variational principle. In particular, for the proof of our main results, we follow the lines of Refs.[11,15].

Key words: Singular Trudinger-Moser inequality, Mountain-pass theorem, exponential growth, multiple solutions

中图分类号:

O175.25

薛益民，陈守婷. 含指数增长非线性项的椭圆方程的多解性[J]. 中国科学技术大学学报, 2020, 50(3): 300-311.

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含指数增长非线性项的椭圆方程的多解性

Multiplicity of solutions to elliptic equations with exponential nonlinearities

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