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We prove the existence of weak solutions for some quasilinear elliptic reaction-diffusion systems with Dirichlet boundary conditions and satisfying to the two main properties: the positivity of the solutions and the balance law. The nonlinearity we consider here has critical growth with respect to the gradient and the data are in  L  1 .

Existence for Some Quasilinear Elliptic Systems with Critical Growth Nonlinearity and L 1 Data