### 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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