Smoothness of Generalized Solutions of a Boundary-Value Problem for a Second-Order Differential-Difference Equation with Mixed Boundary Conditions

被引：0

作者：

N. O. Ivanov ^{[1
]}

机构：

[1] RUDN University, Moscow

来源：

Journal of Mathematical Sciences | 2024年 / 285卷 / 4期

关键词：

boundary-value problem; differential-difference equations; generalized solutions;

D O I：

10.1007/s10958-024-07458-6

中图分类号：

学科分类号：

摘要：

We consider a boundary-value problem with mixed boundary conditions for a second-order differential-difference equation on a finite interval (0, d). We prove existence of a generalized solution of the problem and study the conditions on the right-hand side of the differential-difference equation ensuring the smoothness of the generalized solution over the entire interval. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.

引用

页码：478 / 495

页数：17

共 19 条

[1]

Sh A., Adkhamova and A. L. Skubachevskii, On one damping problem for a nonstationary control system with aftereffect, Sovrem. Mat. Fundam. Napravl, 65, 4, pp. 547-556, (2019)

[2]

Sh A., Adkhamova and A. L. Skubachevskii, On the damping of a control system with aftereffect of a neutral type, Dokl. RAN. Ser. Mat. Inform. Prots. Upr, 490, pp. 81-84, (2020)

[3]

Kamenskii A.G., Boundary-value problems for equations with formally symmetric differentialdifference operators, Diff. Uravn, 12, 5, pp. 815-824, (1976)

[4]

Kamenskii G.A., Myshkis A.D., On the formulation of boundary-value problems for differential equations with deviating argument and several higher-order terms, Diff. Uravn, 10, 3, pp. 409-418, (1974)

[5]

Kamenskii G.A., Myshkis A.D., Skubachevskii A.L., On smooth solutions of a boundary value problem for a differential-difference equation of neutral type, Ukr. Mat. Zh, 37, 5, pp. 581-585, (1985)

[6]

Krasovskii N.N., Theory of Motion Control. Linear Systems, (1968)

[7]

Kryazhimskii A.V., Maksimov V.I., Osipov Y., About positional modeling in dynamic systems, Prikl. Mat. Mekh, 47, 6, pp. 883-890, (1983)

[8]

Liiko V.V., Skubachevskii A.L., Strongly elliptic differential-difference equations with mixed boundary conditions in a cylindrical domain, Sovrem. Mat. Fundam. Napravl, 65, 4, pp. 635-654, (2019)

[9]

Liiko V.V., Skubachevskii A.L., Mixed problems for strongly elliptic differential-difference equations in a cylinder, Mat. Zametki, 107, 5, pp. 693-716, (2020)

[10]

Neverova D.A., Generalized and classical solutions to the second and third boundary-value problem for differential-difference equations, Funct. Differ. Equ, 21, pp. 47-65, (2014)

← 1 2 →