Uniqueness of positive solutions of the Choquard type equations

Abstract

In this paper, by developing Lieb’s methods, we establish uniqueness of the positive radial solutions to the following solitary Choquard type equation

This, together with Ma and Zhao’s classification results, enables us to show the uniqueness of the positive solutions when .

Keywords:

• Choquard type equation
• positive solutions
• uniqueness
• comparison and contraction technique

AMS Subject Classifications:

• 35Q55
• 34A12

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

Research was supported partially by the National Natural Science Foundation of P. R. China [grant number 11171098], [grant number 11571371]; the Hunan Provincial NSF [grant number 11JJ1001].