## Differential and Integral Equations

### Positive solutions of an elliptic system depending on two parameters

Flavio Dickstein

#### Abstract

We consider the Dirichlet problem associated to a $2\times 2$ semilinear elliptic system of equations in a bounded domain of $\mathbb R^n$. This system depends on two parameters $(\eta,\mu)$ and the nonlinear terms are of power type. The existence of solutions for such a problem in the plane $(\eta,\mu)$ is discussed. Our results are natural extensions of those obtained for the corresponding nonlinear eigenvalue problem for elliptic scalar equations.

#### Article information

Source
Differential Integral Equations, Volume 18, Number 3 (2005), 287-297.

Dates
First available in Project Euclid: 21 December 2012

https://projecteuclid.org/euclid.die/1356060220

Mathematical Reviews number (MathSciNet)
MR2122721

Zentralblatt MATH identifier
1212.35032

Subjects
Primary: 35J55
Secondary: 35J60: Nonlinear elliptic equations 35P30: Nonlinear eigenvalue problems, nonlinear spectral theory

#### Citation

Dickstein, Flavio. Positive solutions of an elliptic system depending on two parameters. Differential Integral Equations 18 (2005), no. 3, 287--297. https://projecteuclid.org/euclid.die/1356060220