Mutual spectrum of commutating conjugate operators and correctness and stability criteria for differential-operator equations

• Date: 1991
• Main Authors: Shklyar , A. Ya., Шкляр , А. Я.
• Format: Article
• Language: Russian
• Published: Institute of Mathematics, NAS of Ukraine 1991
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/9623
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

Tests are established for the propriety of the Cauchy problem, the stability, stabilization, asymptotic stability, and exponential stability for the equation $y'' + By' + By = 0, t \in [0, +\infty)$, where $A$ and $B$ are arbitrary commuting self-adjoint operators on a sep...