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

Vetro, Francesca; Winkert, Patrick

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(⋅)-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.
Published in: Applied Mathematics and Optimization, 10.1007/s00245-022-09892-x, Springer Nature