Tatiyana Barinova and Alexander Kostin
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