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We establish a precise connection between two elliptic quasilinear problems with Dirichlet data in a bounded domain of R N : The ...rst one, of the form involves a source gradient term with natural growth, where is nonnegative, > 0; f (x) = 0, and is a nonnegative measure. The second one, of the form presents a source term of order 0; where g is nondecreasing, and is a nonnegative measure. Here and g can present an asymptote. The correlation gives new results of existence, nonexistence,doi:10.1142/s0219199710003993 fatcat:4dqst3yijzfavlrnphglytsi2e