Electron. J. Diff. Eqns., Vol. 2000(2000), No. 12, pp. 1-37.

A singular ODE related to quasilinear elliptic equations

Luka Korkut, Mervan Pasic, & Darko Zubrinic

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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Luka Korkut (e-mail: luka.korkut@fer.hr)
Mervan Pasic (e-mail: mervan.pasic@fer.hr)
Darko Zubrinic (e-mail: darko.zubrinic@fer.hr)
Department of mathematics
Faculty of Electrical Engineering and Computing
Unska 3, 10000 Zagreb, Croatia
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