Abstract and Applied Analysis

Abstract and Applied Analysis / 2000 / Article

Open Access

Volume 5 |Article ID 835093 | 15 pages | https://doi.org/10.1155/S1085337500000324

Solvability of quasilinear elliptic equations with strong dependence on the gradient

Received30 May 2000


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.

Copyright © 2000 Hindawi Publishing Corporation. 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.

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