Generalized critical Kirchhoff-type potential systems with Neumann Boundary conditions

In this paper, we consider a class of quasilinear stationary Kirchhoff type potential systems with Neumann Boundary conditions, which involves general variable exponent elliptic operator critical growth. Under some suitable conditions on the nonlinearities, establish existence and multiplicity solutions for problem by using concentration-compactness principle Lions exponents mountain pass theorem without Palais–Smale condition.