Annali di Matematica Pura ed Applicata

, Volume 119, Issue 1, pp 25–40 | Cite as

On the oscillatory and asymptotic behavior of the bounded solutions of differential equations with deviating arguments

  • Ch. G. Philos
Article

Summary

This paper is dealing with the oscillatory and asymptotic behavior of the bounded solutions of n-th order (n>1) differential equations with deviating arguments involving the so called r-derivatives D r (i)x (i=0, 1, ..., n) of the unknown function x defined by
, where ri (i=1, 2, ..., n−1) are positive continuous functions on the interval [t 0 , ∞). The fundamental purpose is to find a necessary and sufficient condition in order to have at least one (bounded nonoscillatory) solution whose the limit at ∞ exists inR−{0}.

Keywords

Differential Equation Continuous Function Asymptotic Behavior Unknown Function Positive Continuous Function 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    W. A. Coppel,Disconjugacy, Lecture Notes in Mathematics 220, Springer-Verlag, 1971.Google Scholar
  2. [2]
    T. Kusano -H. Onose,Asymptotic behavior of nonoscillatory solutions of functional differential equations of arbitrary order, J. London Math. Soc.,14 (1976), pp. 106–112.MathSciNetGoogle Scholar
  3. [3]
    T. Kusano -H. Onose,Nonoscillation theorems for differential equations with deviating argument, Pacific J. Math.,63 (1976), pp. 185–192.MathSciNetGoogle Scholar
  4. [4]
    Ch. G. Philos,Oscillatory and asymptotic behavior of the bounded solutions of differential equations with deviating arguments, Hiroshima Math. J.,8 (1978), pp. 31–48.MATHMathSciNetGoogle Scholar
  5. [5]
    Ch. G. Philos,An oscillatory and asymptotic classification of the solutions of differential equations with deviating arguments, Atti Accad. Naz. Lincei, Rend. Cl. Sci. Fis. Mat. Natur.,63 (1977), pp. 195–203.MathSciNetGoogle Scholar
  6. [6]
    Ch. G. Philos,Oscillatory and asymptotic behavior of all solutions of differential equations with deviating arguments, Proc. Roy. Soc. Edinburgh Sect. A, in press.Google Scholar
  7. [7]
    Ch. G. Philos - V. A. Staikos,Non-slow oscillations with damping, University of Ioannina, Technical Report no. 92, March 1977.Google Scholar
  8. [8]
    Ch. G. Philos - V. A. Staikos,Quick oscillations with damping, Math. Nachr., to appear.Google Scholar
  9. [9]
    J. Schauder, Der Fixpunktsatz in Funktionalräumen, Studia Math.,2 (1930), pp. 171–180.MATHGoogle Scholar
  10. [10]
    V. A. Staikos,Differential equations with deviating arguments. Oscillation theory (unpublished manuscripts).Google Scholar
  11. [11]
    V. A. Staikos -Ch. G. Philos,On the asymptotic behavior of nonoscillatory solutions of differential equations with deviating arguments, Hiroshima Math. J.,7 (1977), pp. 9–31.MathSciNetGoogle Scholar
  12. [12]
    V. A. Staikos -Ch. G. Philos,Asymptotic properties of nonoscillatory solutions of differential equations with deviating argument, Pacific J. Math.,70 (1977), pp. 221–242.MathSciNetGoogle Scholar
  13. [13]
    V. A. Staikos -Ch. G. Philos,Nonoscillatory phenomena and damped oscillations, Non linear Analysis, Theory, Methods and Applications,2 (1977), pp. 197–210.CrossRefMathSciNetGoogle Scholar
  14. [14]
    W. F. Trench,Oscillation properties of perturbed disconjugate equations, Proc. Amer. Math. Soc.,52 (1975), pp. 147–155.CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Fondazione Annali di Matematika Pura ed Applicata 1979

Authors and Affiliations

  • Ch. G. Philos
    • 1
  1. 1.IoanninaGreece

Personalised recommendations