On the limits of solutions of functional differential equations

Mihály Pituk

Mathematica Bohemica (1993)

  • Volume: 118, Issue: 1, page 53-66
  • ISSN: 0862-7959

Abstract

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Our aim in this paper is to obtain sufficient conditions under which for every ξ ∈ R n there exists a solution x of the functional differential equation x ˙ ( t ) = ∫ c t [ d s Q ( t , s ) ] f ( t , x ( s ) ) , t ∈ [ t 0 , T ] such that l i m t → T - x ( t ) = ξ .

How to cite

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Pituk, Mihály. "On the limits of solutions of functional differential equations." Mathematica Bohemica 118.1 (1993): 53-66. <http://eudml.org/doc/29169>.

@article{Pituk1993,
abstract = {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 $.},
author = {Pituk, Mihály},
journal = {Mathematica Bohemica},
keywords = {completeness; functional differential equation; solution; delay; completeness; functional differential equation},
language = {eng},
number = {1},
pages = {53-66},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the limits of solutions of functional differential equations},
url = {http://eudml.org/doc/29169},
volume = {118},
year = {1993},
}

TY - JOUR
AU - Pituk, Mihály
TI - On the limits of solutions of functional differential equations
JO - Mathematica Bohemica
PY - 1993
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 118
IS - 1
SP - 53
EP - 66
AB - 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 $.
LA - eng
KW - completeness; functional differential equation; solution; delay; completeness; functional differential equation
UR - http://eudml.org/doc/29169
ER -

References

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  1. R. D. Driver, 10.1137/1010058, SIAM Rev. 10(1968), 329-341. (1968) Zbl0165.42801MR0234091DOI10.1137/1010058
  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. (1979) MR0680602
  3. I. Győri, 10.1016/0362-546X(84)90083-X, Nonlinear Anal. 8 (1984), 429-439. (1984) MR0741599DOI10.1016/0362-546X(84)90083-X
  4. I. Győri, I. P. Stavroulakis, Positive solutions of functional differential equations, Boll. Un. Mat. Ital. B (7) 3 (1989), 185-198. (1989) MR0997338
  5. J. Hale, Theory of Functional Differential Equations, Springer-Verlag, New York, 1977. (1977) Zbl0352.34001MR0508721
  6. P. Hartman, Ordinary Differential Equations, John Wiley & Sons, New York-London-Sydney, 1964; Russian transl., Izdatel'stvo "Mir", Moscow. (1964) Zbl0125.32102MR0171038
  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. (1975) Zbl0319.34066MR0454264
  8. V. M. Popov, 10.1016/0022-0396(72)90066-6, J. Differential Equations 11 (1972), 541-561. (1972) MR0296455DOI10.1016/0022-0396(72)90066-6
  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.) (1965) MR0211010
  10. M. Švec, Some properties of functional differential equations, Boll. Un. Mat. Ital. (4) 11 Suppl. fasc. 3 (1975), 467-477. (1975) MR0430476
  11. M. Švec, Some problems concerning the equivalence of two systems of differential equations, Proceedings Equadiff 6 Brno (1985), 171-179. (1985) MR0877120
  12. A. M. Zverkin, Pointwise completeness of systems with delay, Differentsial'nye Uravneniya 9 (1973), 430-436. (In Russian.) (1973) MR0316855

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