Positive solutions of an elliptic system depending on two parameters. (Q976597)

The Dirichlet problem associated to a \(2\mathrel \times 2\) semilinear elliptic system of equations in a bounded domain of \(\mathbb R^n\) is considered. 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. The results are natural extensions of those obtained for the corresponding nonlinear eigenvalue problem for elliptic scalar equations.