## Differential and Integral Equations

### Elliptic equations with singularity on the boundary

#### Abstract

The existence and nonexistence of positive classical solutions is discussed for $-\Delta u = K(x) (1-|x|)^{- \alpha} u^{\beta}$ in the unit ball $B$ with Dirichlet boundary condition ${u |_{\partial B}= 0 }$. Our main tools are based on the variational method and Pohozaev's identity. The singularity of coefficients on the boundary will be handled with the symmetry of functions and some approximation procedures.

#### Article information

Source
Differential Integral Equations, Volume 12, Number 3 (1999), 339-349.

Dates
First available in Project Euclid: 29 April 2013