Georgian Mathematical Journal

, Volume 2, Issue 4, pp 395–418 | Cite as

On proper oscillatory and vanishing-at-infinity solutions of differential equations with a deviating argument

  • I. Kiguradze
  • D. Chichua


Sufficient conditions are found for the existence of multiparametric families of proper oscillatory and vanishing-at-infinity solutions of the differential equation
$$u^{(n)} (t) = g\left( {t, u(\tau _0 (t)), \ldots ,u^{(m - 1)} (\tau _{m - 1} (t))} \right)$$
, wheren≥4,m is the integer part of π/2,g:R+×R m R is a function satisfying the local Carathéodory conditions, and τ i :R+R(i=0,...,m−1) are measurable functions such that τ i (t) →+∞ fort→+∞(i=0,...,m−1).

1991 Mathematics Subject Classification

34K15 34K10 

Key words and phrases

Functional differential equation proper solution oscillatory solution vanishing-at-infinity solution 


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Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • I. Kiguradze
    • 1
  • D. Chichua
    • 2
  1. 1.A. Razmadze Mathematical InstituteGeorgian Academy of SciencesTbilisiRepublic of Georgia
  2. 2.I. Vekua Institute of Applied MathematicsTbilisi State UniversityTbilisiRepublic of Georgia

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