| Title:
|
Stability and correctness of abstract differential equations in Hilbert spaces (English) |
| Author:
|
Barták, Jaroslav |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
28 |
| Issue:
|
4 |
| Year:
|
1978 |
| Pages:
|
548-593 |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| MSC:
|
34G05 |
| idZBL:
|
Zbl 0409.34057 |
| idMR:
|
MR0499545 |
| DOI:
|
10.21136/CMJ.1978.101561 |
| . |
| Date available:
|
2008-06-09T14:30:30Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/101561 |
| . |
| Reference:
|
[1] Barták J.: Lyapunov stability and stability at constantly acting disturbances of an abstract differential equatiçn of the second order.Czech. Math. J., 26 (101) 1976, 411 - 437. MR 0415017 |
| Reference:
|
[2] Barták J.: The Lyapunov stability of the Timoshenko type equation.Časopis pro pěstování matematiky, roč. 101, 1976, 130-139. MR 0445073 |
| Reference:
|
[3] Daleckij Ju. L., Krejn M. G.: Ustojčivosť rešenij differencialnych uravnenij v Banachovom prostranstve.Izdat2lstvo ''Nauka", Moskva 1970, (Russian). |
| Reference:
|
[4] Davis S. H., Kerczek Ch.: A reformulation of energy stability theory.Arch. Rat. Mech. Anal., Vol 52, No 2, 1973, 112-117. Zbl 0272.76028, MR 1553571, 10.1007/BF00282321 |
| Reference:
|
[5] Derguzov V. I.: Ob ustojčivosti rešenij uravněnij Gamiltona s neogranicennymi periodičeskimi operatornymi koeficientami.Matematičeskij sbornik, T. 63 (105), No 4, 1964, 591 - 619, (Russian). MR 0163022 |
| Reference:
|
[6] Derguzov V. I.: Dostatočnyje uslovija ustojčivosti gamiltonovych uravněnij s neogranicennymi periodičeskimi operatornymi koeficientami.Matematičeskij sbornik, T. 64 (106), No 2, 1964, 419-435, (Russian). MR 0167693 |
| Reference:
|
[7] Domšlak Ju. I.: К teorii differencialnych uravněnij v Banachovom prostranstve s postojannym neogranicennym operatorom.DAN Az. SSR, Tom XVIII, No 5, 1962, 3 - 6 (Russian). |
| Reference:
|
[8] Fink J. P., Hall W. S., Hausrath A. R.: A convergent two-time method for periodic differential equations.J. Diff. Eq., Vol. 15, No 3, 1974, 459-498. Zbl 0258.34042, MR 0344620, 10.1016/0022-0396(74)90068-0 |
| Reference:
|
[9] Chalilov Z. I.: Ob ustojčivosti rešenij uravněnija v Banachovom prostranstve.DAN SSSR, Tom 137, No 4, 1961, 797-799, (Russian). |
| Reference:
|
[10] Chalilov Z. I.: Ob ustojčivosti rešenij evoljucionnovo uravněnija s neograničennym operatorom.DAN Az. SSR, Tom XVII, No 2, 1961, 91-95, (Russian). |
| Reference:
|
[11] Joseph D. D., Sattinger D. H.: Bifurcating time periodic solutions and their stability.Arch. Rat. Mech. Anal., Vol. 45, No 2, 1972, 79-109. Zbl 0239.76057, MR 0387844, 10.1007/BF00253039 |
| Reference:
|
[12] Kielhöfer H.: Stability and semilinear evolution equations in Hilbert space.Arch. Rat. Mech. Anal., Vol. 57, No 2, 1974, 150-165. MR 0442405, 10.1007/BF00248417 |
| Reference:
|
[13] Kurzweil J.: Exponentially stable integral manifolds.averaging principle and continuous dependence on a parameter, Czech. Math. J., 16 (91), 1966, No 3, 4, 380-423, 463 - 492. Zbl 0186.47701, MR 0206440 |
| Reference:
|
[14] Leipholz H. H. E.: Stability of elastic rods via Liapunov's second method.Ingenieur - Archiv 44, 1975, 21-26. Zbl 0295.73041, MR 0421234 |
| Reference:
|
[15] Malkin L G.: Teorija ustojcivosti dvizenija.Gosudarstvennoje izdatelstvo techniko-teoreticeskoj literatury, Moskva-Leningrad 1952, (Russian). |
| Reference:
|
[16] Nachlinger R. R., Faust C. D.: On the stability of a linearly viscoelastic bar.ZAMM 52, 1972, 179-181. Zbl 0255.73060, MR 0307574, 10.1002/zamm.19720520310 |
| Reference:
|
[17] Neustupa J.: The uniform exponential stability and the uniform stability at constantly acting disturbances of a periodic solution of a wave equation.Czech. Math. J., 26 (101), 1976, 388-410. Zbl 0346.35012, MR 0435565 |
| Reference:
|
[18] Parks P. С.: А stability criterion for panel flutter via the second method of Liapunov.AIAA Journal, 1966, 175-177. 10.2514/3.3412 |
| Reference:
|
[19] Park P. C.: A stability criterion for a panel flutter problem via the second method of Liapunov.Diff. Eq. Dynam. Systems, 1967, 287-298. |
| Reference:
|
[20] Prodi G.: Teoremi di tipo locale per 11 sistema di Navier-Stokes a stabilité delle soluzioni stazionarie.Rend. Sem. Matematico, Université di Padova, Vol. XXXII, 1962, 374-397. MR 0189354 |
| Reference:
|
[21] Sattinger D. H.: Topics in stability and bifurcation theory.Lecture Notes in Mathematics, 309, Springer-Verlag, Berlin-Heidelberg-New York, 1973. Zbl 0248.35003, MR 0463624 |
| Reference:
|
[22] Serrin J.: On the stability of viscous fluid motions.Arch. Rat. Mech. Anal., Vol. 5, No 1, 1959, 1-13. Zbl 0086.20001, MR 0105250, 10.1007/BF00284160 |
| Reference:
|
[23] Sova M.: On the Timoshenko type equations.Časopis pro pěstování matematiky, svazek 100, číslo 3, 1975, 217-254. Zbl 0324.34060, MR 0387763 |
| Reference:
|
[24] Sova M.: Linear diff'erential equations in Banach spaces.Rozpravy ČSAV, řada matematických a přírodních věd. Vol. 85, sešit 6, Academia Praha, 1975. MR 0481342 |
| Reference:
|
[25] Straškraba I., Vejvoda O.: Periodic solutions to abstract diff'erential equations.Czech. Math. J., 23 (98), 1973, 635-669. MR 0499577 |
| Reference:
|
[26] Zenkovskaja S. M.: Ob ustojcivosti odnovo periodiceskovo resenija uravnenija Navje-Stoksa.Prikl. Mat. Meh., vyp. 1, 1967, 124-130, (Russian). MR 0218729 |
| . |
