Luka Korkut, Mervan Pasic, & Darko Zubrinic
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.
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