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Original Articles

Multiple solutions for a class of fractional quasi-linear equations with critical exponential growth in ℝN

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Pages 969-983 | Received 24 Aug 2015, Accepted 08 Dec 2015, Published online: 26 Apr 2016
 

Abstract

This paper deals with a class of non-local equations involving the fractional p-Laplacian, where the non-linear term is assumed to have critical exponential growth. More specifically, by applying variational methods together with a suitable Trudinger-Moser inequality for fractional Sobolev space, we obtain the existence of at least two positive weak solutions.

Acknowledgements

The authors would like to thank the anonymous reviewers and the editor for their helpful comments.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

Project Supported by the National Natural Science Foundation of China [grant number 11571093], [grant number 11471164]; project on Graduate Students Education and Innovation of Jiangsu Province [grant number KYZZ0209]; A Project Funded by the Priority Academic Program Development of Jiangsu Highed Education Institutions (PAPD).

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