Existence and Uniqueness of Solutions for the p(x)-Laplacian Equation with Convection Term

Bin-Sheng Wang, Gang-Ling Hou, Bin Ge
2020 Mathematics  
In this paper, we consider the existence and uniqueness of solutions for a quasilinear elliptic equation with a variable exponent and a reaction term depending on the gradient. Based on the surjectivity result for pseudomonotone operators, we prove the existence of at least one weak solution of such a problem. Furthermore, we obtain the uniqueness of the solution for the above problem under some considerations. Our results generalize and improve the existing results.
doi:10.3390/math8101768 fatcat:lw7apw4sgnbfzfxu3xw2fypzea