Differential and Integral Equations

Positive solutions of an elliptic system depending on two parameters

Flavio Dickstein

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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

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

First available in Project Euclid: 21 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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

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