Best Ulam constants for damped linear oscillators with variable coefficients

Abstract

An associated Riccati equation is used to study the Ulam stability of non-autonomous linear differential equations that model the damped linear oscillator. In particular, the best (minimal) Ulam constants for these equations are derived. These robust results apply to equations with solutions that blow up in finite time, as well as to equations with solutions that exist globally on $(-\infty ,\infty )$. Illustrative, non-trivial examples are presented, highlighting the main results.