Correctness of the Cauchy problem for trinomial higher-order operator differential equations

• Date: 1993
• Main Authors: Shklyar, A. Ya., Шкляр, А. Я.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 1993
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/5857
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

Criteria are established for the correctness of the Cauchy problem for the equations $y^{(2n)} + Ay^{(n)} + By = 0, \quad t \in [0, \infty)$ where $n > 1, А, В$ are arbitrary commuting self-adjoint operators in a Hilbert space. For $n = 2$, the criterion is illustrated by the example of the e...