Abstract and Applied Analysis
Volume 5 (2000), Issue 3, Pages 159-173

Solvability of quasilinear elliptic equations with strong dependence on the gradient

Darko Žubrinić

Department of Applied Mathematics, Faculty of Electrical Engineering and Computing, Unska 3, Zagreb 10000, Croatia

Received 30 May 2000

Copyright © 2000 Darko Žubrinić. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.