Multiplicity of solutions to elliptic equations with exponential nonlinearities

doi:10.3969/j.issn.0253-2778.2020.03.007

Journal of University of Science and Technology of China ›› 2020, Vol. 50 ›› Issue (3): 300-311.DOI: 10.3969/j.issn.0253-2778.2020.03.007

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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).

Abstract

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

CLC Number:

O175.25

References

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Multiplicity of solutions to elliptic equations with exponential nonlinearities

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