Existence and multiplicity results for a class of anisotropic Robin elliptic problems

Abstract

The aim of this paper is to study a class of anisotropic Robin elliptic equations with variable exponents where the nonlinearity may depend on the gradient of the solution. First, we demonstrate the existence of at least one weak solution using the surjectivity result of pseudomonotone operators. Moreover, under additional conditions on the data, we show that the solution is unique. Furthermore, we prove the existence of at least three weak solutions using the direct Ricceri variational principle when the nonlinearity does not depend on the gradient.