engleski

A singular ODE related to quasilinear elliptic equations

We consider a quasilinear elliptic problem with the natural growth in the gradient. Existence, non-existence, uniqueness, and qualitative properties od 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 equations.

p-Laplacian ; spherically symetric ; existence ; non-existence ; uniqueness ; comparison principle ; singular ODE ; regularity.

nije evidentirano