## Multiplicity of solutions for a singular $p$-laplacian elliptic equation

### Volume 99 / 2010

Annales Polonici Mathematici 99 (2010), 157-180
MSC: Primary 35J25; Secondary 35J75.
DOI: 10.4064/ap99-2-4

#### Abstract

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.