The existence of two continuous solutions for a nonlinear singular elliptic equation with natural growth in the gradient is proved for the Dirichlet problem in the unit ball centered at the origin. The first continuous solution is positive and maximal; it is obtained via the regularization method. The second continuous solution is zero at the origin, and follows by considering the corresponding radial ODE and by sub-sup solutions method.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap99-2-4,
author = {Wen-shu Zhou and Xiao-dan Wei},
title = {Multiplicity of solutions for a singular p-laplacian elliptic equation},
journal = {Annales Polonici Mathematici},
volume = {98},
year = {2010},
pages = {157-180},
zbl = {1209.35052},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap99-2-4}
}
Wen-shu Zhou; Xiao-dan Wei. Multiplicity of solutions for a singular p-laplacian elliptic equation. Annales Polonici Mathematici, Tome 98 (2010) pp. 157-180. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap99-2-4/