Geodesic
Specific asymptotic stability of solutions to a linear homogeneous Volterra integro-differential equation of the fourth order
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2021), pp. 22-28 
S. Iskandarov; E. A. Komartsova. Specific asymptotic stability of solutions to a linear homogeneous Volterra integro-differential equation of the fourth order. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2021), pp. 22-28. http://geodesic.mathdoc.fr/item/VMUMM_2021_1_a3/
@article{VMUMM_2021_1_a3,
     author = {S. Iskandarov and E. A. Komartsova},
     title = {Specific asymptotic stability of solutions to a linear homogeneous {Volterra} integro-differential equation of the fourth order},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {22--28},
     year = {2021},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2021_1_a3/}
}
TY  - JOUR
AU  - S. Iskandarov
AU  - E. A. Komartsova
TI  - Specific asymptotic stability of solutions to a linear homogeneous Volterra integro-differential equation of the fourth order
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2021
SP  - 22
EP  - 28
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2021_1_a3/
LA  - ru
ID  - VMUMM_2021_1_a3
ER  - 
%0 Journal Article
%A S. Iskandarov
%A E. A. Komartsova
%T Specific asymptotic stability of solutions to a linear homogeneous Volterra integro-differential equation of the fourth order
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2021
%P 22-28
%N 1
%U http://geodesic.mathdoc.fr/item/VMUMM_2021_1_a3/
%G ru
%F VMUMM_2021_1_a3

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

Sufficient conditions for asymptotic stability of solutions to a homogeneous fourth order linear integro-differential Volterra equation are established in the case when any nonzero solution to the corresponding homogeneous fourth order linear differential equation is not asymptotically stable. An illustrative example is presented.

[1] Iskandarov S., Zhaparova Z.A., “Spetsificheskaya eksponentsialnaya ustoichivost reshenii lineinogo odnorodnogo volterrova integro-differentsialnogo uravneniya chetvertogo poryadka”, Vestn. KNU im. Zh. Balasagyna. Ser. 3. Estestv.-tekhn. nauki. Matematika. Informatika. Kibernetika, 2010, no. 4, 27–37

[2] Zhaparova Z.A., “Spetsificheskaya asimptoticheskaya ustoichivost reshenii lineinogo odnorodnogo volterrova integro-differentsialnogo uravneniya chetvertogo poryadka”, Issled. po integro-differents. uravneniyam, 45, Ilim, Bishkek, 2012, 25–33

[3] Iskandarov S., “O novom variante metoda nestandartnogo svedeniya k sisteme dlya lineinogo volterrova integro-differentsialnogo uravneniya tretego poryadka”, Issled. po integro-differents. uravneniyam, 37, Ilim, Bishkek, 2007, 24–29

[4] Iskandarov S., Metod vesovykh i srezyvayuschikh funktsii i asimptoticheskie svoistva reshenii integro-differentsialnykh i integralnykh uravnenii tipa Volterra, Ilim, Bishkek, 2002

[5] Iskandarov S., Shabdanov D.N., “Metod chastichnogo srezyvaniya i ogranichennost reshenii neyavnogo volterrova integro-differentsialnogo uravneniya pervogo poryadka”, Issled. po integro-differents. uravneniyam, 33, Ilim, Bishkek, 2004, 67–71

[6] Lyusternik L.A., Sobolev V.I., Elementy funktsionalnogo analiza, Nauka, M., 1965

[7] Iskandarov S., “Ob odnom nestandartnom metode issledovaniya asimptoticheskoi ustoichivosti reshenii lineinogo volterrova integro-differentsialnogo uravneniya chetvertogo poryadka”, Issled. po integro-differents. uravneniyam, 44, Ilim, Bishkek, 2012, 44–51

[8] Landau E., Vvedenie v differentsialnoe i integralnoe ischislenie, IL, M., 1948

[9] Volterra V., Matematicheskaya teoriya borby za suschestvovanie, Per. s fr., pod red. Yu. M. Svirezheva, Nauka, M., 1976

[10] Ved Yu.A., Pakhyrov Z., “Dostatochnye priznaki ogranichennosti reshenii lineinykh integro-differentsialnykh uravnenii”, Issled. po integro-differents. uravneniyam v Kirgizii, 9, Ilim, Frunze, 1973, 68–103

[11] Imanaliev M.I., Iskandarov S., “Spetsificheskii priznak ustoichivosti reshenii lineinogo odnorodnogo volterrova integro-differentsialnogo uravneniya chetvertogo poryadka”, Dokl. RAH, 425:4 (2009), 447–451