Existence, Uniqueness and Asymptotic Behavior of Parametric Anisotropic (p, q)-Equations with Convection

Source abstract

Abstract In this paper we study anisotropic weighted ( p , q )-equations with a parametric right-hand side depending on the gradient of the solution. Under very general assumptions on the data and by using a topological approach, we prove existence and uniqueness results and study the asymptotic behavior of the solutions when both the $$q(\cdot )$$ q ( · ) -Laplacian on the left-hand side and the reaction term are modulated by a parameter. Moreover, we present some properties of the solution sets with respect to the parameters.