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In this paper, we consider a quasi-linear Dirichlet system with possiblecompeting $(p,q)$-Laplacians and convections. Due to the lack of ellipticity,monotonicity, and variational structure, the standard approaches to theexistence of weak solutions cannot be adopted. Nevertheless, through anapproximation procedure and a corollary of Brouwer's fixed point theorem weshow that the problem admits a solution in a suitable sense.

Quasilinear Dirichlet systems with competing operators and convection