The Second Boundary Value Problem for Differential-Difference Equations

A. L. Skubachevskii^a^,^b^,* and N. O. Ivanov^a^,**

^aMathematical Institute of the RUDN University, Moscow, Russia

^bMoscow Center for Fundamental and Applied Mathematics, Lomonosov Moscow State University, Moscow, Russia

Correspondence to: *e-mail: skub@lector.ru
Correspondence to: **e-mail: noivanov1@gmail.com

Received 20 August, 2021

Abstract—We consider the second boundary value problem for a second-order differential-difference equation with variable coefficients on the interval (0, d). It was obtained the necessary and sufficient condition for the existence of a generalized solution. It was proved that, if the right-hand side of the equation is orthogonal in ${{L}_{2}}(0,d)$ to some functions, then a generalized solution from the Sobolev space $W_{2}^{1}(0,d)$ belongs to the space $W_{2}^{2}(0,d)$.

Keywords: differential–difference equations, generalized solutions, boundary value problem

DOI: 10.1134/S106456242105015X