Existence result for variable exponents elliptic system with lack of compactness

Abstract

In this article, we prove the existence of a solution for nonlinear system governed by $\left(p\right(x),q(x\left)\right)$-Laplacian operators by using the concentration-compactness Principle for recovering the lack of compactness and some variable techniques.

COMMUNICATED BY:

• M. A. Ragusa

Keywords:

• $p\left(x\right)$-Laplacian
• variable exponent
• sobolev space
• concentration-compactness principle
• critical exponent
• Ekeland variational principle
• dirichlet problem

2010 Mathematics Subject Classifications:

• 35J50
• 35J60
• 35J61

Acknowledgements

The authors would like to thank the referees and editors for their pertinent comments and suggestions which improve the quality of present manuscript.

Disclosure statement

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