OSCILLATION CRITERIA FOR FIRST ORDER LINEAR DIFFERENTIAL EQUATIONS WITH RETARDED ARGUMENTS DEPENDING ON THE UNKNOWN FUNCTION
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.
$$
x'(t)+p(t)x(\Delta(t,x(t)))=0
$$
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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