Existence and uniqueness results for Kirchhoff–Schrödinger–Poisson system with general singularity

Abstract

In this paper, under the general singular assumptions on f, we discuss the existence and uniqueness of solution to a class of Kirchhoff–Schrödinger–Poisson system. For the existence of solution, we assume that f is nonincreasing on and satisfies general singularity at zero, and sublinear growth at infinity. Furthermore, we also obtain the unique result assuming that f satisfies one side Lipschitz condition on . The variational method is employed to discuss the existence and uniqueness of solution to this system.

Keywords:

• Kirchhoff–Schrödinger–Poisson
• general singularity
• uniqueness
• variational method

AMS Subject Classifications:

• 35J75
• 35J50

Acknowledgements

The authors express their gratitude to the reviewers for careful reading and helpful suggestions which led to an improvement of the original manuscript.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

Projects supported by National Natural Science Foundation of China [grant number 11301313], [grant number 11571209], [grant number 11671239]; Science Council of Shanxi Province [grant number 2013021001-4], [grant number 2014021009-01], [grant number 2015021007]; Scientific and Technological of Higher Education Institutions in Shanxi [grant number 2015101], [grant number 2016106].