## Differential and Integral Equations

### Multiple solutions for semilinear elliptic systems involving critical Sobolev exponent

Michinori Ishiwata

#### Abstract

The effect of the domain topology on the multiplicity of solutions for a semilinear elliptic system with critical Sobolev exponent is discussed. We show that if the coupling term is sufficiently small, then there exist at least cat $\Omega$ positive solutions, where cat denotes the Ljusternik-Schnirelman category.

#### Article information

Source
Differential Integral Equations Volume 20, Number 11 (2007), 1237-1252.

Dates
First available in Project Euclid: 20 December 2012