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

Author

Listed:
  • Gennadii V. Demidenko

    (Laboratory of Differential and Difference Equations, Sobolev Institute of Mathematics, 4, Acad. Koptyug Avenue, 630090 Novosibirsk, Russia)

  • Inessa I. Matveeva

    (Laboratory of Differential and Difference Equations, Sobolev Institute of Mathematics, 4, Acad. Koptyug Avenue, 630090 Novosibirsk, Russia)

Abstract

We consider a class of second-order 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 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.

Suggested Citation

  • Gennadii V. Demidenko & Inessa I. Matveeva, 2021. "Asymptotic Stability of Solutions to a Class of Second-Order Delay Differential Equations," Mathematics, MDPI, vol. 9(16), pages 1-13, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1847-:d:608768
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