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 u ( n ) ( t ) = f ( t , u ( τ 1 ( t ) ) , ⋯ , u ( n - 1 ) ( τ n ( t ) ) ) , where the vector function f : ] a , b [ × R k n → R k 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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  2. Sur l’equation differentielle lineaire de second ordre. Détermination d’une integrale par deux valeurs assignées. Extension aux équations d’ordre n , J. Math. pures et appl. 8, No 2 (1929), 125-144. 
  3. On a singular multi-point boundary value problem, Ann. Mat. Pura ed Appl. 86(1970), 367-399. Zbl0251.34012MR0271449
  4. Some singular boundary value problems for ordinary differential equations, Tbilisi: Tbilisi University Press (1975) (in Russian). Zbl0521.34019MR0499402
  5. On some singular boundary value problems for ordinary differential equations, Equadiff 5 Proc. 5 Czech. Conf. Diff. Equations and Appl. Leipzig: Teubner Verlagsgesselschaft (1982), 174-178. Zbl0521.34019
  6. On the solvability of the Valée-Poussin problem, Differentsial’nyje Uravnenija 21, No 3 (1985), 391-398. MR0785447
  7. On a boundary value problems for higher ordinary differential equations with singularities, Uspekhi Mat. Nauk 41, No. 4 (1986), 166-167 (in Russian). 
  8. On the two-point boundary value problems for systems of higher order ordinary differential equations with singularities, Georgian Math. J. 1, No 1(1994), 31-45. 
  9. L’existence et l’unicité des solutions du probléme d’interpolation differentielle ordinaire d’ordre n , Ann. Polon. Math. 15, No 3(1964), 253-271. MR0173804
  10. Nonoscillatory solutions of equation x ( n ) + p 1 ( t ) x ( n - 1 ) + ⋯ + p n ( t ) x = 0 , Uspekhi Mat. Nauk 24, No 2(1969), 43-96 (in Russian). 
  11. On a multi-point boundary value problem, Nauchnie Dokl. Vis. Shkoli 5 (1958), 34-37 (in Russian). 
  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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