ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. 69, 2 (2000)
pp. 183-198

POSITIVE SOLUTIONS OF QUASILINEAR ELLIPTIC SYSTEMS WITH STRONG DEPENDENCE ON THE GRADIENT
D. ZUBRINIC

Abstract. We study existence and nonexistence of positive, spherically symmetric solutions of diagonal quasilinear elliptic systems involving equations with\break $p$-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 nonsolvability 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.

AMS subject classification. 35J55, 45J05
Keywords. Quasilinear elliptic system, positive solution, spherically symmetric

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Acta Mathematica Universitatis Comenianae
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Faculty of Mathematics, Physics and Informatics
Comenius University
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