Geodesic
Generalized Solutions of the Second Boundary-Value Problem for Differential-Difference Equations with Variable Coefficients on Intervals of Noninteger Length
Matematičeskie zametki, Tome 111 (2022) no. 6, pp. 873-886.

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper deals with the second boundary-value problem for a second-order differential-difference equation with variable coefficients on the interval $(0,d)$ as well as with the question of conditions on the right-hand side of the equation that ensure the smoothness of the generalized solutions of the boundary-value problem on the whole interval $(0,d)$ for $d \notin \mathbb{N}$.
Keywords: differential-difference equations, generalized solutions, boundary-value problem. 
@article{MZM_2022_111_6_a6,
     author = {A. L. Skubachevskii and N. O. Ivanov},
     title = {Generalized {Solutions} of the {Second} {Boundary-Value} {Problem} for {Differential-Difference} {Equations} with {Variable} {Coefficients} on {Intervals} of {Noninteger} {Length}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {873--886},
     publisher = {mathdoc},
     volume = {111},
     number = {6},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2022_111_6_a6/}
}
TY  - JOUR
AU  - A. L. Skubachevskii
AU  - N. O. Ivanov
TI  - Generalized Solutions of the Second Boundary-Value Problem for Differential-Difference Equations with Variable Coefficients on Intervals of Noninteger Length
JO  - Matematičeskie zametki
PY  - 2022
SP  - 873
EP  - 886
VL  - 111
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2022_111_6_a6/
LA  - ru
ID  - MZM_2022_111_6_a6
ER  - 
%0 Journal Article
%A A. L. Skubachevskii
%A N. O. Ivanov
%T Generalized Solutions of the Second Boundary-Value Problem for Differential-Difference Equations with Variable Coefficients on Intervals of Noninteger Length
%J Matematičeskie zametki
%D 2022
%P 873-886
%V 111
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2022_111_6_a6/
%G ru
%F MZM_2022_111_6_a6
A. L. Skubachevskii; N. O. Ivanov. Generalized Solutions of the Second Boundary-Value Problem for Differential-Difference Equations with Variable Coefficients on Intervals of Noninteger Length. Matematičeskie zametki, Tome 111 (2022) no. 6, pp. 873-886. http://geodesic.mathdoc.fr/item/MZM_2022_111_6_a6/

[1] Yu. S. Osipov, “O stabilizatsii upravlyaemykh sistem s zapazdyvaniem”, Differents. uravneniya, 1:5 (1965), 605–618 | MR | Zbl

[2] N. N. Krasovskii, Teoriya upravleniya dvizheniya. Lineinye sistemy, Nauka, M., 1968 | MR | Zbl

[3] A. V. Kryazhimskii, V. I. Maksimov, Yu. S. Osipov, “O pozitsionnom modelirovanii v dinamicheskikh sistemakh”, Prikl. matem. mekh., 47:6 (1983), 883–890 | MR

[4] A. L. Skubachevskii, “K zadache ob uspokoenii sistemy upravleniya s posledeistviem”, Dokl. AN, 335:2 (1994), 157–160 | MR | Zbl

[5] A. L. Skubachevskii, Elliptic Functional Differential Equations and Applications, Birkhäuser, Basel, 1997 | MR | Zbl

[6] G. A. Kamenskii, A. D. Myshkis, “K postanovke kraevykh zadach dlya differentsialnykh uravnenii s otklonyayuschimsya argumentom i neskolkimi starshimi chlenami”, Differents. uravneniya, 10:3 (1974), 409–418 | MR | Zbl

[7] A. G. Kamenskii, “Kraevye zadachi dlya uravnenii s formalno simmetrichnymi differentsialno-raznostnymi operatorami”, Differents. uravneniya, 12:5 (1976), 815–824 | MR | Zbl

[8] D. A. Neverova, A. L. Skubachevskii, “O klassicheskikh i obobschennykh resheniyakh kraevykh zadach dlya differentsialno-raznostnykh uravnenii s peremennymi koeffitsientami”, Matem. zametki, 94:5 (2013), 702–719 | DOI | MR | Zbl

[9] D. A. Neverova, “Generalized and classical solutions to the second and third boundary-value problem for differential-difference equations”, Funct. Differ. Equ., 21:1-2 (2014), 47–65 | MR | Zbl

[10] G. A. Kamenskii, A. D. Myshkis, A. L. Skubachevskii, “O gladkikh resheniyakh kraevoi zadachi dlya differentsialno-raznostnogo uravneniya neitralnogo tipa”, Ukr. matem. zhurn., 37:5 (1985), 581–589 | MR | Zbl

[11] V. V. Liiko, A. L. Skubachevskii, “Smeshannye zadachi dlya silno ellipticheskikh differentsialno-raznostnykh uravnenii v tsilindre”, Matem. zametki, 107:5 (2020), 693–716 | DOI | MR | Zbl

[12] A. L. Skubachevskii, N. O. Ivanov, “Ob obobschennykh resheniyakh vtoroi kraevoi zadachi dlya differentsialno-raznostnykh uravnenii s peremennymi koeffitsientami”, SMFN, 67, no. 3, Rossiiskii universitet druzhby narodov, M., 2021, 576–595 | DOI

[13] A. L. Skubachevskii, N. O. Ivanov, “Vtoraya kraevaya zadacha dlya differentsialno-raznostnykh uravnenii”, Dokl. AN, 500:1 (2021), 74–77 | DOI | Zbl