Non-interlaced solutions of 2-dimensional systems of linear ordinary differential equations (Q2839313)

The authors study the asymptotic behavior of solutions of two-dimensional systems of linear ordinary differential equations NEWLINE\[NEWLINE \frac{dY}{dx} = A(x) Y + B(x), NEWLINE\]NEWLINE where \(Y \in {\mathbb R}^2\) and \(A, \;B: (0,a) \to M_{2\times 2}({\mathbb R})\) are \(C^1\) and may admit singularities at \(x=0\). The main result establishes some equivalence between interlace, noninterlace as well as \(o\)-minimality of solutions of these systems and the solutions of the corresponding Riccati equations at \(x=0\).