Geodesic
The second boundary value problem for differential-difference equations
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 500 (2021), pp. 74-77

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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 $W^1_2(0,d)$ belongs to the space $W_2^2(0,d)$.
Keywords: differential–difference equations, generalized solutions, boundary value problem. 
@article{DANMA_2021_500_a13,
     author = {A. L. Skubachevskii and N. O. Ivanov},
     title = {The second boundary value problem for differential-difference equations},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {74--77},
     publisher = {mathdoc},
     volume = {500},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2021_500_a13/}
}
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A. L. Skubachevskii; N. O. Ivanov. The second boundary value problem for differential-difference equations. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 500 (2021), pp. 74-77. http://geodesic.mathdoc.fr/item/DANMA_2021_500_a13/