General conditions guaranteeing the solvability of the Cauchy problem for functional differential equations

N. Dilna; A. Rontó

Mathematica Bohemica (2008)

  • Volume: 133, Issue: 4, page 435-445
  • ISSN: 0862-7959

Abstract

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New general unique solvability conditions of the Cauchy problem for systems of general linear functional differential equations are established. The class of equations considered covers, in particular, linear equations with transformed argument, integro-differential equations, neutral type equations and their systems of an arbitrary order.

How to cite

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Dilna, N., and Rontó, A.. "General conditions guaranteeing the solvability of the Cauchy problem for functional differential equations." Mathematica Bohemica 133.4 (2008): 435-445. <http://eudml.org/doc/250537>.

@article{Dilna2008,
abstract = {New general unique solvability conditions of the Cauchy problem for systems of general linear functional differential equations are established. The class of equations considered covers, in particular, linear equations with transformed argument, integro-differential equations, neutral type equations and their systems of an arbitrary order.},
author = {Dilna, N., Rontó, A.},
journal = {Mathematica Bohemica},
keywords = {functional differential equation; Cauchy problem; initial value problem; differential inequality; functional differential equation; Cauchy problem; initial value problem; differential inequality},
language = {eng},
number = {4},
pages = {435-445},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {General conditions guaranteeing the solvability of the Cauchy problem for functional differential equations},
url = {http://eudml.org/doc/250537},
volume = {133},
year = {2008},
}

TY - JOUR
AU - Dilna, N.
AU - Rontó, A.
TI - General conditions guaranteeing the solvability of the Cauchy problem for functional differential equations
JO - Mathematica Bohemica
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 133
IS - 4
SP - 435
EP - 445
AB - New general unique solvability conditions of the Cauchy problem for systems of general linear functional differential equations are established. The class of equations considered covers, in particular, linear equations with transformed argument, integro-differential equations, neutral type equations and their systems of an arbitrary order.
LA - eng
KW - functional differential equation; Cauchy problem; initial value problem; differential inequality; functional differential equation; Cauchy problem; initial value problem; differential inequality
UR - http://eudml.org/doc/250537
ER -

References

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  1. Azbelev, N., Maksimov, V., Rakhmatullina, L., Introduction to the Theory of Linear Functional Differential Equations, Advanced Series in Mathematical Science and Engineering, vol. 3, World Federation Publishers Company, Atlanta, GA (1995). (1995) Zbl0867.34051MR1422013
  2. Azbelev, N. V., Rakhmatullina, L. F., Theory of linear abstract functional-differential equations and applications, Mem. Differential Equations Math. Phys. 8 (1996), 1-102. (1996) Zbl0870.34067MR1432626
  3. Hakl, R., Lomtatidze, A., Půža, B., On a boundary value problem for first-order scalar functional differential equations, Nonlinear Anal. 53 (2003), 391-405. (2003) Zbl1024.34056MR1964333
  4. Hartman, P., Ordinary Differential Equations, Classics in Applied Mathematics, vol. 38, Philadelphia, PA: SIAM, 2nd ed., unabridged, corrected republication of the 1982 original. ed. (2002). (2002) Zbl1009.34001MR1929104
  5. Krasnoselskii, M. A., Positive Solutions of Operator Equations, Wolters-Noordhoff Scientific Publications, Groningen (1964). (1964) MR0181881
  6. Krasnoselskii, M. A., Lifshits, E. A., Pokornyi, Yu. V., Stetsenko, V. Ya., Positively invertible linear operators and the solvability of non-linear equations, Russian Dokl. Akad. Nauk Tadzhik. SSR 17 (1974), 12-14. (1974) MR0358427
  7. Krasnoselskii, M. A., Zabreiko, P. P., Geometrical Methods of Nonlinear Analysis, Springer, Berlin (1984). (1984) MR0736839
  8. Šremr, J., On the Cauchy type problem for systems of functional differential equations, Nonlinear Anal. 67 3240-3260 (2007). (2007) Zbl1130.34035MR2350882

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