Asymptotic Stability of Solutions to a Class of Second-Order Delay Differential Equations

Asymptotic Stability of Solutions to a Class of Second-Order Delay Differential Equations

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We consider a class of second-order Jandy Levolor Parts nonlinear delay differential equations with periodic coefficients in linear terms.We obtain conditions under which the zero solution is asymptotically stable.Estimates for attraction sets and decay rates Mittens of solutions at infinity are established.

This class of equations includes the equation of vibrations of the inverted pendulum, the suspension point of which performs arbitrary periodic oscillations along the vertical line.