Journal of Inequalities and Applications
Volume 1 (1997), Issue 1, Pages 47-71

Radial solutions of equations and inequalities involving the p-Laplacian

Wolfgang Reichel and Wolfgang Walter

Mathematisches Institut I, Universität Karlsruhe, Karlsruhe D-76128, Germany

Received 31 July 1996

Copyright © 1997 Wolfgang Reichel and Wolfgang Walter. 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.


Several problems for the differential equation Lpαu=g(r,u)withLpαu=rα(rα|u|p2u) are considered. For α=N1, the operator Lpα is the radially symmetric p-Laplacian in N. For the initial value problem with given data u(r0)=u0,u(r0)=u0 various uniqueness conditions and counterexamples to uniqueness are given. For the case where g is increasing in u, a sharp comparison theorem is established; it leads to maximal solutions, nonuniqueness and uniqueness results, among others. Using these results, a strong comparison principle for the boundary value problem and a number of properties of blow-up solutions are proved under weak assumptions on the nonlinearity g(r,u).