An existence result for singular nonlocal fractional Kirchhoff–Schrödinger–Poisson system

Abstract

In this paper, we study the existence of infinitely many weak solutions to a fractional Kirchhoff–Schrödinger–Poisson system involving a weak singularity, i.e. when $0<\gamma <1$. Further, we obtain the existence of a solution with a strong singularity, i.e. when $\gamma >1$. We employ variational techniques to prove the existence and multiplicity results. Moreover, an $L^{\mathrm{\infty }}$ estimate is obtained by using the Moser iteration method.

Keywords:

• Fractional Sobolev space
• genus
• symmetric mountain pass theorem
• Nehari manifold
• singularity

AMS SUBJECT CLASSIFICATIONS:

• 35R11
• 35J75
• 35J20
• 35J60
• 35J10

Acknowledgements

The author thanks the anonymous referee(s) and the editor(s) for their careful reading, comments and constructive remarks toward improving the manuscript. The author also thanks Prof. D. Choudhuri for his guidance, suggestions and discussions during the preparation of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The author would like to thank the Council of Scientific and Industrial Research (CSIR), India for the financial assistantship to carry out this research work [grant number 09/983(0013)/2017-EMR-I].