### Nonuniqueness of solutions for Dirichlet problems related to fully nonlinear singular or degenerate operators

Françoise Demengel

#### Abstract

We study the Dirichlet problem for fully nonlinear elliptic operators: $G(D^2u, \nabla u, u, x) = f(x)$ in $\Omega$, where $\Omega$ is a bounded regular domain, and $f$ is continuous. We prove the existence, the nonexistence and the multiplicity of solutions for some particular right-hand side $f$ when $G$ has its two principal eigenvalues of different sign.

#### Article information

Source
Adv. Differential Equations Volume 14, Number 11/12 (2009), 1107-1126.

Dates
First available in Project Euclid: 18 December 2012