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 with critical growth and real positive parameter. We show that the problem has at least one solution, which converges to zero in the norm of the space as the real positive parameter tends to infinity, via combining the truncation technique, variational method, and the concentration–compactness principle for variable exponent under suitable assumptions on the nonlinearities.

The Dirichlet Problem for a Class of Anisotropic Schrödinger-Kirchhoff-Type Equations With Critical Exponent

“…, N }. For further study of problems with critical exponents, we refer the reader to [2,3,4,6,7,8,10,14,15,16,17], and the references therein.…”