engleski

Positive solutions of quasilinear elliptic systems with strong dependence on the gradient

We study existence and nonexistence of positive symmetric solutions of diagonal quasilinear elliptic systems involving equations with p-Laplacians, and with strong dependence on the gradient on the right-hand side. The existence proof is constructive, with solutions possessing explicit integral representation. Also, we obtain critical exponents of the gradient. We introduce the notion of cyclic elliptic systems in order to study nonsolvabiliy of general elliptic systems. The elliptic system is studied by relating it to the corresponding system of singular ordinary integro-differential equations of the first order.

quasilinear elliptic system; positive solution. spherically symmetric

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