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

  • Xing WangEmail author
  • Li Zhang
Article
  • 5 Downloads

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.

Keywords

Fractional Laplacian nondifferentiable functional existence and multiple 

Mathematics Subject Classification

35J25 47J30 46E35 

Notes

Acknowledgements

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

Compliance with ethical standards

Conflict of interests

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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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of ScienceXi’an University of TechnologyXi’anPeople’s Republic of China
  2. 2.School of ScienceChang’an UniversityXi’anPeople’s Republic of China

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