Regularization of two-term differential equations with singular coefficients by quasiderivatives

• Date: 2011
• Main Authors: Goryunov, A. S., Mikhailets, V. A., Горюнов, А. С., Михайлец, В. А.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2011
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2797
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We propose a regularization of the formal differential expression $$l(y) = i^m y^{(m)}(t) + q(t)y(t),\; t \in (a, b),$$ of order $m \geq 3$ by using quasiderivatives. It is assumed that the distribution coefficient $q$ has an antiderivative $Q \in L ([a, b]; \mathbb{C})$. In the symmetric case $(Q...