Abstract
In this paper, we consider a class of quasilinear stationary Kirchhoff type potential systems with Neumann Boundary conditions, which involves a general variable exponent elliptic operator with critical growth. Under some suitable conditions on the nonlinearities, we establish existence and multiplicity of solutions for the problem by using the concentration-compactness principle of Lions for variable exponents and the mountain pass theorem without the Palais–Smale condition.
Acknowledgements
The second author wish to thank GNAMPA and the RUDN University Strategic Academic Leadership Program.
Disclosure statement
No potential conflict of interest was reported by the author(s).