Annali di Matematica Pura ed Applicata

, Volume 119, Issue 1, pp 25–40

# 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

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