Existence of Steady States. Positive and Nontrivial Steady States

Abstract

Let us consider in Cⁿ the nonlinear equation

$\displaystyle Ax = F(x), \quad\quad (1.1)$

where A is an invertible matrix, F continuously maps Ω (r) into Cⁿ for a positive r ≤ ∞. Recall that ∥ . ∥ is the Euclidean norm and $\Omega (r) = \{x\in\mbox{C}^n : \parallel x\parallel \leq r\}$.