Geodesic
Criteria for the boundness of the solutions of the Cauchy problem for a~sistem of hyperbolic difference equations
Izvestiya. Mathematics , Tome 5 (1971) no. 3, pp. 711-718.

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

In the present article the difference analog of the Cauchy problem for a system of hyperbolic equations of second order is discussed. Conditions for the boundedness (for arbitrary bounded right-hand sides) of the solution of this problem are established for the case where the coefficients are constants or have weak variation at infinity. 
@article{IM2_1971_5_3_a11,
     author = {R. K. Romanovskii and A. M. Biberman},
     title = {Criteria for the boundness of the solutions of the {Cauchy} problem for a~sistem of hyperbolic difference equations},
     journal = {Izvestiya. Mathematics },
     pages = {711--718},
     publisher = {mathdoc},
     volume = {5},
     number = {3},
     year = {1971},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1971_5_3_a11/}
}
TY  - JOUR
AU  - R. K. Romanovskii
AU  - A. M. Biberman
TI  - Criteria for the boundness of the solutions of the Cauchy problem for a~sistem of hyperbolic difference equations
JO  - Izvestiya. Mathematics 
PY  - 1971
SP  - 711
EP  - 718
VL  - 5
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1971_5_3_a11/
LA  - en
ID  - IM2_1971_5_3_a11
ER  - 
%0 Journal Article
%A R. K. Romanovskii
%A A. M. Biberman
%T Criteria for the boundness of the solutions of the Cauchy problem for a~sistem of hyperbolic difference equations
%J Izvestiya. Mathematics 
%D 1971
%P 711-718
%V 5
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1971_5_3_a11/
%G en
%F IM2_1971_5_3_a11
R. K. Romanovskii; A. M. Biberman. Criteria for the boundness of the solutions of the Cauchy problem for a~sistem of hyperbolic difference equations. Izvestiya. Mathematics , Tome 5 (1971) no. 3, pp. 711-718. http://geodesic.mathdoc.fr/item/IM2_1971_5_3_a11/

[1] Rutman M. A., “Kriterii ogranichennosti reshenii dlya lineinykh differentsialnykh uravnenii s chastnymi proizvodnymi, obladayuschim starshim chlenom”, Dokl. AN SSSR, 147:4 (1962), 789–792 | MR | Zbl

[2] Rutman M. A., “Ob ogranichennosti reshenii nekotorykh lineinykh uravnenii v chastnykh raznostyakh”, Dokl. AN SSSR, 159:2 (1964), 273–275 | MR | Zbl

[3] Rutman M. A., “O nekotorykh operatornykh uravneniyakh v poluuporyadochennom prostranstve, imeyuschikh primenenie v teorii ustoichivosti po Lyapunovu”, Dokl. AN SSSR, 101:2 (1955), 217–220 | MR | Zbl

[4] Marmershtein I. I., “Ob ogranichennosti reshenii nekotorykh sistem lineinykh uravnenii v chastnykh raznostyakh”, Dokl. AN SSSR, 189:3 (1969), 475–478

[5] Romanovskii R. K., “Ob ustoichivosti reshenii zadachi Koshi dlya lineinykh differentsialnykh uravnenii giperbolicheskogo tipa”, Dokl. AN SSSR, 163:5 (1965), 1077–1080 | MR | Zbl

[6] Romanovskii R. K., “Priznaki ogranichennosti reshenii odnoi smeshannoi kraevoi zadachi dlya giperbolicheskogo uravneniya II poryadka v banakhovom prostranstve”, Izv. VUZov. Matematika, 1969, no. 1, 60–66 | MR | Zbl

[7] Romanovskii R. K., Avtoreferat kandidatskoi dissertatsii, Kiev, 1969

[8] Persidskii K. P., “Ob odnoi teoreme ustoichivosti dvizheniya, 1”, Izv. fiz.-mat. ob-va pri Kazanskom universitete, 8:3 (1936–1937), 47–86