Narrow region principle and Liouville type results for fractional Lane–Emden system

Abstract

In this paper, narrow region principle for cooperative systems involving fractional Laplacian is developed. As an application, some Liouville type results of the fractional Lane–Emden system(1)

are obtained via the method of moving planes. Different to the conventional method by studying the equivalent integral system, we work directly on the differential system. Our method can also be employed to obtain Liouville type results for general cooperative systems involving fractional Laplacian.

Keywords:

• Fractional Lane–Emden system
• narrow region principle
• moving planes
• radial symmetry
• non-existence

AMS Subject Classifications:

• 35J60
• 53C21
• 58J05

Acknowledgements

We thank the unknown referee for helpful suggestions and thank Profs. W. Chen and L. Ma for guidance.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by National Science Foundation [grant number 11271111].