صندلی اداری

OSCILLATION CRITERIA FOR FIRST ORDER LINEAR DIFFERENTIAL EQUATIONS WITH RETARDED ARGUMENTS DEPENDING ON THE UNKNOWN FUNCTION

N.T. Markova, P.S. Simeonov

Abstract


In this paper differential equations of the type
$$
x'(t)+p(t)x(\Delta(t,x(t)))=0
$$
and
$$
x'(t)+\sum_{i=1}^m p_i(t)x(\Delta_i(t,x(t)))=0
$$
are considered, where $p(t)\ge 0$, $p_i(t)\ge 0$, $i=1,\dots,m$ and the retarded arguments $\Delta$, $\Delta_i$, $i=1,\dots,m$ depend on the independent variable $t$ as well as on the unknown function $x$.

Sufficient conditions are found under which these equations are oscillatory.

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