Exact bounds for exponential dichotomy roughness. I: Strong dichotomy
The author considers the unperturbed and perturbed equations (1) \(x'=A(t)x\) and (2) \(y'=[A(t)+B(t)]y,\) where \(t\in {\mathbb{R}}_+\) and A and B are \(n\times n\) matrices. It is shown that if (1) has strong dichotomy on \({\mathbb{R}}_+\), then (2) also has a dichotomy and exact estimates on the exponential dichotomy roughness are obtained.
scientific article; zbMATH DE number 4061706