Parametric anisotropic elliptic problems with variable exponents and convection terms

In this paper, we study a class of parametric anisotropic elliptic equations with variable exponents where the nonlinearity may depend on the gradient of the solution. We prove the existence of the solution using the surjectivity result of pseudomonotone operators, and under additional conditions on the data, we show that the solution is unique. Moreover, we establish the existence of at least three weak solutions using the direct Ricceri variational principle when the nonlinearity does not depend on the gradient.