(p(x),q(x))-Kirchhoff-Type Problems Involving Logarithmic Nonlinearity with Variable Exponent and Convection Term

Abstract

In the present article, we study a class of Kirchhoff-type equations driven by the (p(x),q(x))-Laplacian. Due to the lack of a variational structure, ellipticity, and monotonicity, the well-known variational methods are not applicable. With the help of the Galerkin method and Brezis theorem, we obtain the existence of finite-dimensional approximate solutions and weak solutions. One of the main difficulties and innovations of the present article is that we consider competing (p(x),q(x))-Laplacian, convective terms, and logarithmic nonlinearity with variable exponents, another one is the weaker assumptions on nonlocal term Mυ(x) and nonlinear term g.