Existence of solutions for a perturbed p-Laplacian system with critical exponent in

Abstract

In this paper, we consider the following perturbed p-Laplacian system

where , , satisfy , denotes the critical Sobolev exponent. Under some mild conditions on V, g and h, we show that the problem has at least one positive weak solution provided , where is a sufficiently small positive number. Moreover, in X as

Keywords:

• Existence
• perturbed
• p-Laplacian system
• critical exponent

AMS Subject Classifications:

• 35B30
• 35J65
• 35J92

Acknowledgements

The authors would like to express sincere thanks to the anonymous referee for his/her carefully reading the manuscript and valuable comments and suggestions.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was Supported by the National Natural Science Foundation of China [grant number 11571093], [grant number 11471164]; project on Graduate Students Education and Innovation of Jiangsu Province [grant number KYZZ_0209]