Tatiyana Barinova and Alexander Kostin

On Asymptotic Stability of Solutions of Second Order Linear Nonautonomous Differential Equations

abstract:
The sufficient conditions for asymptotic stability of solutions of second order linear differential equation
$$ y''+p(t)y'+q(t)y=0 $$
with continuously differentiable coefficients $p:[0,+\infty)\to\R$ and $q:[0,+\infty) \linebreak \to\R$ are established in the case where the roots of the characteristic equation
$$ \lambda^2+p(t)\lambda+q(t)=0 $$
satisfy conditions
$$ \RRe\lambda_i(t)<0 \;\;\text{for}\;\; t\geq 0, \quad \int\limits_{t_0}^{+\infty} \RRe\lambda_i(t)\,dt=-\infty \;\; (i=1,2). $$

Mathematics Subject Classification: 34D05, 34E10

Key words and phrases: Second order differential equation, linear, nonautonomous, asymptotic stability