Tatiyana Barinova and Alexander Kostin

Sufficiency Conditions for Asymptotic Stability of Solutions of a Linear Homogeneous Nonautonomous Differential Equation of Second Order

The problem on the stability of second order linear homogeneous differential equation
$$ y''+p(t)y'+q(t)y=0 $$
is investigated in the case where the roots $\lambda_i(t)$ $(i=1,2)$ of the characteristic equation
$$ \lambda^2+p(t)\lambda+q(t)=0 $$
are such that
$$ \lambda_i(t)<0 \;\;\text{for}\;\; t\geq t_0, \quad \int\limits_{t_0}^{+\infty} \lambda_i(t)\,dt=-\infty \;\; (i=1,2) $$
and there exist finite or infinite limits $\lim\limits_{t\to+\infty}\lambda_i(t)$ $(i=1,2)$.

Mathematics Subject Classification: 34D05, 34E10

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