The dirichlet problem for a class of anisotropic Schrödinger-Kirchhoff-type equations with critical exponent

Abstract

In this paper, our focus lies in addressing the Dirichlet problem associated with a specific class of critical anisotropic elliptic equations of Schrödinger-Kirchhoff type. These equations incorporate variable exponents and a real positive parameter. Our objective is to establish the existence of at least one solution to this problem.

Keywords

• Schrodinger-Kirchhoff-type problems
• Dirichlet boundary conditions
• p(x)-Laplacian
• Anisotropic variable exponent Sobolev spaces
• Concentration-compactness principle
• parameter