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

Fractal and Fractional

Yingjie Li¹  Tianqing An²  Weichun Bu²  Deliang Qian³ 

[1] College of Primary Education, Fuyang Preschool Teachers College, Fuyang 236015, China;College of Science, Hohai University, Nanjing 210098, China;College of Science, Zhongyuan University of Technology, Zhengzhou 450007, China;

关键词: Kirchhoff-type equations;    logarithmic nonlinearity;    convection term;    Galerkin method;    Brezis theorem;   

DOI  :  10.3390/fractalfract6050255

来源: DOAJ

【 摘 要 】

In the present article, we study a class of Kirchhoff-type equations driven by the $\left(p\right(x),q(x\left)\right)$-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 $\left(p\right(x),q(x\left)\right)$-Laplacian, convective terms, and logarithmic nonlinearity with variable exponents, another one is the weaker assumptions on nonlocal term $M_{\upsilon \left(x\right)}$ and nonlinear term g.

【 授权许可】

Unknown