STABILITY FOR LINEAR SCALAR FUNCTIONAL DIFFERENTIAL EQUATIONS WITH TWO DELAYS
Abstract
In this paper, we consider mainly the following linear scalar functional differential equation with two discrete delays
\[
x^{\prime }(t)=a(t)x(t)+b(t)x(t-r_{1})+c(t)x(t-r_{2}),~t \geq t
t_{0},
\]
where $a$, $b$, $c\in C([t_{0},\infty ),\mathbb{R})$ and
$r_{1}>0$, $r_{2}>0$ are constants. Several Wazewski-type
inequalities of solutions are obtained. As a consequence, we
derive some sufficient conditions ensuring that the zero solution
of the equation is asymptotically stable under the condition $a\left( t\right) \geq 0$ and the zero solution of
the equation is unstable under the condition $a\left( t\right)
\leq 0$.
\[
x^{\prime }(t)=a(t)x(t)+b(t)x(t-r_{1})+c(t)x(t-r_{2}),~t \geq t
t_{0},
\]
where $a$, $b$, $c\in C([t_{0},\infty ),\mathbb{R})$ and
$r_{1}>0$, $r_{2}>0$ are constants. Several Wazewski-type
inequalities of solutions are obtained. As a consequence, we
derive some sufficient conditions ensuring that the zero solution
of the equation is asymptotically stable under the condition $a\left( t\right) \geq 0$ and the zero solution of
the equation is unstable under the condition $a\left( t\right)
\leq 0$.
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