Electronic Journal of Differential Equations,
Vol. 2000(2000), No. 12, pp. 1-37.

Title: A singular ODE related to quasilinear elliptic equations

Authors: Luka Korkut (Unska, Zagreb, Croatia)
 Mervan Pasic (Unska, Zagreb, Croatia)
 Darko  Zubrinic (Unska, Zagreb, Croatia)

Abstract: 
 We consider a quasilinear elliptic problem with the natural growth in the
 gradient.  Existence, non-existence, uniqueness, and qualitative properties of
 positive solutions are obtained.  We consider both weak and strong solutions.
 All results are based on the study of a suitable singular ODE of the first
 order.  We also introduce a comparison principle for a class of nonlinear
 integral operators of Volterra type that enables to obtain uniqueness of weak
 solutions of the quasilinear equation.  

Submitted September 10, 1999. Published February 12, 2000.
Math Subject Classifications: 35J60, 35B65, 34C10.
Key Words: p-Laplacian; spherically symmetric; existence; non-existence;
           uniqueness; comparison principle; singular ODE; regularity.