Existence and asymptotic properties for quasilinear elliptic equations with gradient dependence

Abstract

The paper focuses on a Dirichlet problem driven by the (p,q)-Laplacian containing a parameter $mu$ in the principal part of the elliptic equation and a (convection) term fully depending on the solution and its gradient. Existence of solutions, uniqueness, a priori estimates, and asymptotic properties as $mu o 0$ and $mu o infty$ are established under suitable conditions.