Frozen time methods for conditionally stable problems in singular perturbation theory (Q1325245)

The author obtains an asymptotic estimate of the Green function for the singularly perturbed linear system \(\mu x'= A(t)x\), where \(\mu\) is a small parameter. The matrix function \(A(t)\) is defined on \(\mathbb{R}\) and is assumed to satisfy the following properties: 1) \(A(t)\) is a function of class \(C^ 1\) and \(\| A(t)\|\leq M\), \(\| A'(t)\|\leq \beta\) for \(t\in\mathbb{R}\). 2) For each \(t\in \mathbb{R}\), \(k\) eigenvalues of \(A(t)\) satisfy \(\text{Re }\lambda(t)\leq -\gamma\), and \(n-k\) eigenvalues satisfy \(\text{Re }\lambda(t)\geq\gamma\).