| Title:
|
On the limits of solutions of functional differential equations (English) |
| Author:
|
Pituk, Michal |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
118 |
| Issue:
|
1 |
| Year:
|
1993 |
| Pages:
|
53-66 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Our aim in this paper is to obtain sufficient conditions under which for every $\xi \in R^n$ there exists a solution $x$ of the functional differential equation $\dot{x}(t)=\int^t_c[d_sQ(t,s)]f(t,x(s)),\ t\in [t_0,T]$ such that $lim_{t\rightarrow T-}x(t)=\xi$. (English) |
| Keyword:
|
completeness |
| Keyword:
|
functional differential equation |
| Keyword:
|
solution |
| Keyword:
|
delay |
| MSC:
|
34K25 |
| idZBL:
|
Zbl 0778.34056 |
| idMR:
|
MR1213833 |
| DOI:
|
10.21136/MB.1993.126015 |
| . |
| Date available:
|
2009-09-24T20:57:16Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126015 |
| . |
| Reference:
|
[1] R. D. Driver: On Ryabov's asymptotic characterization of the solutions of quasi-linear differential equations with small delays.SIAM Rev. 10(1968), 329-341. Zbl 0165.42801, MR 0234091, 10.1137/1010058 |
| Reference:
|
[2] I. Győri: On existence of the limits of solutions of functional differential equations.Colloquia Mathematica Societatis János Bolyai 30. Qualitative Theory of Differential Equations, Szeged (Hungary), (1979), North-Holland Publ. Company, Amsterdam, (1980), 325-362. MR 0680602 |
| Reference:
|
[3] I. Győri: On the oscillatory behaviour of solutions of certain nonlinear and linear delay differential equations.Nonlinear Anal. 8 (1984), 429-439. MR 0741599, 10.1016/0362-546X(84)90083-X |
| Reference:
|
[4] I. Győri, I. P. Stavroulakis: Positive solutions of functional differential equations.Boll. Un. Mat. Ital. B (7) 3 (1989), 185-198. MR 0997338 |
| Reference:
|
[5] J. Hale: Theory of Functional Differential Equations.Springer-Verlag, New York, 1977. Zbl 0352.34001, MR 0508721 |
| Reference:
|
[6] P. Hartman: Ordinary Differential Equations.John Wiley & Sons, New York-London-Sydney, 1964; Russian transl., Izdatel'stvo "Mir", Moscow. Zbl 0125.32102, MR 0171038 |
| Reference:
|
[7] J. Jarník, J. Kurzweil: Ryabov's special solutions of functional differential equations.Boll. Un. Mat. Ital. (4) 11 Suppl. fasc. 3 (1975), 198-208. Zbl 0319.34066, MR 0454264 |
| Reference:
|
[8] V. M. Popov: Pointwise degenaracy of linear time-invariant delay differential equations.J. Differential Equations 11 (1972), 541-561. MR 0296455, 10.1016/0022-0396(72)90066-6 |
| Reference:
|
[9] Yu. A. Ryabov: Certain asymptotic properties of linear systems with small time lag.Trudy Sem. Teor. Differencial. Uravnenii s Otklon. Argumentom Univ. Druzby Narodov Patrisa Lumumby 3 (1965), 153-164. (In Russian.) MR 0211010 |
| Reference:
|
[10] M. Švec: Some properties of functional differential equations.Boll. Un. Mat. Ital. (4) 11 Suppl. fasc. 3 (1975), 467-477. MR 0430476 |
| Reference:
|
[11] M. Švec: Some problems concerning the equivalence of two systems of differential equations.Proceedings Equadiff 6 Brno (1985), 171-179. MR 0877120 |
| Reference:
|
[12] A. M. Zverkin: Pointwise completeness of systems with delay.Differentsial'nye Uravneniya 9 (1973), 430-436. (In Russian.) MR 0316855 |
| . |
