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Source : Moscow University Ma ... ✕

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On the Method of Lyapunov Functionals for a Linear First-Order Volterra Integrodifferential Equation with Delay on the Semiaxis

Samandar İSKANDAROV

Article | 2023 | Moscow University Mathematics Bulletin78 ( 3 )

Sufficient conditions are established to ensure the estimation, boundedness, power-law absolute integrability on the semiaxis, the tendency to zero under the tendency to infinity of the independent variable of all solutions of the linear Volterra integrodifferential equation of the first order with delay. For this purpose, a generalized Lyapunov functional is constructed. An illustrative example is presented. Keyword: absolute integrability; argument lag; boundedness; estimation; generalized method of Lyapunov functionals; tending to zero of solutions; Volterra integrodifferential equation of the first order

Specific Asymptotic Stability of Solutions to a Linear Homogeneous Volterra Integro-Differential Equation of the Fourth Order

Samandar İSKANDAROV

Article | 2021 | Moscow University Mathematics Bulletin76 ( 1 )

Sufficient conditions for the asymptotic stability of solutions to a fourth-order linear homogeneous Volterra integro-differential equation are established in the case where any nonzero solution to the corresponding linear homogeneous differential equation of the fourth order is not asymptotically stable. An illustrative example is given.