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Existence and Multiplicity of Weak Positive Solutions to a Class of Fractional Laplacian with a Singular Nonlinearity

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Abstract

This paper is devoted to the study of a class of fractional Laplacian with a singular nonlinearity. The purpose of this article is to give the existence and multiplicity of weak positive solutions by the combined effects of a superlinear and singular term. It is worth pointing out that the testing function in the definition of weak positive solutions does not need to have compact support in bounded domain. Hence the results of this paper are new even in the fractional Laplacian case.

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Acknowledgements

The authors are very grateful to the referees for their helpful suggestions and comments which have improved the paper.

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Authors and Affiliations

  1. School of Science, Xi’an University of Technology, Xi’an, 710054, Shaanxi, People’s Republic of China

    Xing Wang

  2. School of Science, Chang’an University, Xi’an, 710064, Shaanxi, People’s Republic of China

    Li Zhang

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  1. Xing Wang
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  2. Li Zhang
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Correspondence to Xing Wang.

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The authors declare that there is no conflict of interests regarding the publication of this paper.

Funding

This work is supported by the National Natural Science Foundation of China (Nos. 11801038, 11626185) and Natural Science Foundation of Shaanxi Provincial Department of Education (No. 16KJ1558). This work is also supported by the Project Supported by Natural Science Basic Research Plan in Shaanxi Province of China (Nos. 2017JQ1011, 2018JQ1023).

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Wang, X., Zhang, L. Existence and Multiplicity of Weak Positive Solutions to a Class of Fractional Laplacian with a Singular Nonlinearity. Results Math 74, 81 (2019). https://doi.org/10.1007/s00025-019-1004-0

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  • DOI: https://doi.org/10.1007/s00025-019-1004-0

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