Geodesic
On generalized solutions of the second boundary-value problem for differential-difference equations with variable coefficients
Contemporary Mathematics. Fundamental Directions, Dedicated to 70th anniversary of the President of the RUDN University V. M. Filippov, Tome 67 (2021) no. 3, pp. 576-595 
A. L. Skubachevskii; N. O. Ivanov. On generalized solutions of the second boundary-value problem for differential-difference equations with variable coefficients. Contemporary Mathematics. Fundamental Directions, Dedicated to 70th anniversary of the President of the RUDN University V. M. Filippov, Tome 67 (2021) no. 3, pp. 576-595. http://geodesic.mathdoc.fr/item/CMFD_2021_67_3_a11/
@article{CMFD_2021_67_3_a11,
     author = {A. L. Skubachevskii and N. O. Ivanov},
     title = {On generalized solutions of the second boundary-value problem for differential-difference equations with variable coefficients},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {576--595},
     year = {2021},
     volume = {67},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2021_67_3_a11/}
}
TY  - JOUR
AU  - A. L. Skubachevskii
AU  - N. O. Ivanov
TI  - On generalized solutions of the second boundary-value problem for differential-difference equations with variable coefficients
JO  - Contemporary Mathematics. Fundamental Directions
PY  - 2021
SP  - 576
EP  - 595
VL  - 67
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/CMFD_2021_67_3_a11/
LA  - ru
ID  - CMFD_2021_67_3_a11
ER  - 
%0 Journal Article
%A A. L. Skubachevskii
%A N. O. Ivanov
%T On generalized solutions of the second boundary-value problem for differential-difference equations with variable coefficients
%J Contemporary Mathematics. Fundamental Directions
%D 2021
%P 576-595
%V 67
%N 3
%U http://geodesic.mathdoc.fr/item/CMFD_2021_67_3_a11/
%G ru
%F CMFD_2021_67_3_a11

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We consider the second boundary-value problem for a second-order differential-difference equation with variable coefficients on the interval $(0, d)$. We investigate the existence of a generalized solution and obtain conditions on the right-hand side of the equation which ensure the smoothness of generalized solutions on the entire interval $(0, d)$.

[1] Danford N., Shvarts Dzh., Lineinye operatory. Spektralnaya teoriya. Samosopryazhennye operatory v gilbertovom prostranstve, Mir, M., 1966

[2] Kamenskii A. G., “Kraevye zadachi dlya uravnenii s formalno simmetrichnymi differentsialno-raznostnymi operatorami”, Diff. uravn., 12 (1976), 815–824 | Zbl

[3] Kamenskii G. A., Myshkis A. D., “Postanovka kraevykh zadach dlya differentsialnykh uravnenii s otklonyayuschimisya argumentami v starshikh chlenakh”, Diff. uravn., 10 (1974), 409–418 | Zbl

[4] Kamenskii G. A., Myshkis A. D., Skubachevskii A. L., “O gladkikh resheniyakh kraevoi zadachi dlya differentsialno-raznostnogo uravneniya neitralnogo tipa”, Ukr. mat. zh., 37:5 (1985), 581–585

[5] Kato T., Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972

[6] Krasovskii N. N., Teoriya upravleniya dvizheniem. Lineinye sistemy, Nauka, M., 1968

[7] Krein S. G., Lineinye uravneniya v banakhovykh prostranstvakh, Nauka, M., 1971

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

[9] Lions Zh. L., Madzhenes E., Neodnorodnye granichnye zadachi i ikh prilozheniya, Mir, M., 1971

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

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

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

[13] Elsgolts L. E., Norkin S. B., Vvedenie v teoriyu differentsialnykh uravnenii s otklonyayuschimsya argumentom, Nauka, M., 1971

[14] Neverova D. A., “Generalized and classical solutions to the second and third boundary-value problem for differential-difference equations”, Functional Differential Equations, 21 (2014), 47–65 | Zbl

[15] Skubachevskii A. L., Elliptic Functional Differential Equations and Applications, Birkhäuser, Basel—Boston—Berlin, 1997 | Zbl