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This paper treats the second order quasilinear elliptic system of the form Dpua HOjxjUv a; Dqva KOjxjUu b in R N with nonnegative functions H, K. Su‰cient conditions will be given to have positive radial entire solutions and to have no nonnegative nontrivial radial entire solutions under some restriction on p; q; a and b. When H and K behave like positive constant multiples ofjxj n ; n A R, we can completely characterize the existence property of positive radial entire solutions.

Existence and nonexistence of positive radial entire solutions of second order quasilinear elliptic systems