On the Vallée-Poussin problem for singular differential equations with deviating arguments

Ivan Kiguradze; Bedřich Půža

Archivum Mathematicum (1997)

  • Volume: 033, Issue: 1-2, page 127-138
  • ISSN: 0044-8753

Abstract

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For the differential equation where the vector function has nonintegrable singularities with respect to the first argument, sufficient conditions for existence and uniqueness of the Vallée–Poussin problem are established.

How to cite

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Kiguradze, Ivan, and Půža, Bedřich. "On the Vallée-Poussin problem for singular differential equations with deviating arguments." Archivum Mathematicum 033.1-2 (1997): 127-138. <http://eudml.org/doc/248017>.

@article{Kiguradze1997,
abstract = {For the differential equation \[ u^\{(n)\}(t)= f(t,u(\tau \_\{1\}(t)),\dots ,u^\{(n-1)\}(\tau \_\{n\}(t))), \] where the vector function $ f:\ ]a,b[\,\times \{R\}^\{kn\} \rightarrow \{R\}^\{k\}$ has nonintegrable singularities with respect to the first argument, sufficient conditions for existence and uniqueness of the Vallée–Poussin problem are established.},
author = {Kiguradze, Ivan, Půža, Bedřich},
journal = {Archivum Mathematicum},
keywords = {singular differential equation with deviating arguments; the Valée-Poussin problem; existence theorem; uniqueness theorem; singular differential equations with deviating arguments; Valée-Poussin problem; existence; uniqueness},
language = {eng},
number = {1-2},
pages = {127-138},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On the Vallée-Poussin problem for singular differential equations with deviating arguments},
url = {http://eudml.org/doc/248017},
volume = {033},
year = {1997},
}

TY - JOUR
AU - Kiguradze, Ivan
AU - Půža, Bedřich
TI - On the Vallée-Poussin problem for singular differential equations with deviating arguments
JO - Archivum Mathematicum
PY - 1997
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 033
IS - 1-2
SP - 127
EP - 138
AB - For the differential equation \[ u^{(n)}(t)= f(t,u(\tau _{1}(t)),\dots ,u^{(n-1)}(\tau _{n}(t))), \] where the vector function $ f:\ ]a,b[\,\times {R}^{kn} \rightarrow {R}^{k}$ has nonintegrable singularities with respect to the first argument, sufficient conditions for existence and uniqueness of the Vallée–Poussin problem are established.
LA - eng
KW - singular differential equation with deviating arguments; the Valée-Poussin problem; existence theorem; uniqueness theorem; singular differential equations with deviating arguments; Valée-Poussin problem; existence; uniqueness
UR - http://eudml.org/doc/248017
ER -

References

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  9. L’existence et l’unicité des solutions du probléme d’interpolation differentielle ordinaire d’ordre , Ann. Polon. Math. 15, No 3(1964), 253-271. MR0173804
  10. Nonoscillatory solutions of equation , Uspekhi Mat. Nauk 24, No 2(1969), 43-96 (in Russian). 
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  12. Linear problems for systems of nonlinear differential equations, J. Diff. Equat. 3, No 4(1967), 580-594. Zbl0161.06102MR0216068
  13. Equazioni Differenzialli nel campo reale, Bologna: Zanichelli (1948). MR0026731
  14. On a multipoint boundary value problem for nonlinear ordinary differential equations with singularities, Arch. Math. 30, No 3(1994), 171-206. MR1308353

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