The Neumann problem for a class of generalized Kirchhoff-type potential systems

Abstract In this paper, we are concerned with the Neumann problem for a class of quasilinear stationary Kirchhoff-type potential systems, which involves general variable exponents elliptic operators critical growth and real positive parameter. We show that has at least one solution, converges to zero in norm space as parameter tends infinity, via combining truncation technique, variational method, concentration–compactness principle exponent under suitable assumptions on nonlinearities.