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Solvability of quasilinear elliptic equations with strong dependence on the gradient

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  • Darko Žubrinić

Abstract

We study the problem of existence of positive, spherically symmetric strong solutions of quasilinear elliptic equations involving p -Laplacian in the ball. We allow simultaneous strong dependence of the right-hand side on both the unknown function and its gradient. The elliptic problem is studied by relating it to the corresponding singular ordinary integro-differential equation. Solvability range is obtained in the form of simple inequalities involving the coefficients describing the problem. We also study a posteriori regularity of solutions. An existence result is formulated for elliptic equations on arbitrary bounded domains in dependence of outer radius of domain.

Suggested Citation

  • Darko Žubrinić, 2000. "Solvability of quasilinear elliptic equations with strong dependence on the gradient," Abstract and Applied Analysis, Hindawi, vol. 5, pages 1-15, January.
    • Handle: RePEc:hin:jnlaaa:835093
    DOI: 10.1155/S1085337500000324
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