Existence of solutions for a critical (p₁(x), … , p_n(x))-Kirchhoff-type potential systems

ABSTRACT

In this paper, by using the concentration–compactness principle of Lions for variable exponent spaces and the Mountain Pass Theorem, we obtain the existence of nontrivial solutions for a class of $\left(p_1\right(x),\dots ,p_n(x\left)\right)$-Kirchhoff-type potential systems type with critical exponent.

COMMUNICATED BY:

• M. A. Ragusa

KEYWORDS:

• Variable exponent spaces
• critical Sobolev exponents
• $\left(p_1\right(x)\dots p_n(x\left)\right)$-Kirchhoff-type problems
• concentration–compactness principle
• Palais–Smale condition
• mountain pass theorem
• critical points theory

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 35B33
• 35J50
• 35J60
• 35D30

Acknowledgements

The author wants to express their gratitude to the anonymous referee for the careful reading and helpful comments on the manuscript.

Disclosure statement

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