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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 ...More
Sufficient conditions are established such as the sign of the functions of absolute and quadratic integrability on the half-axis of the components of the solution of a linear system of Volterra-type integral equations of the second kind in the new formulation, namely, without the assumption that the components of the free term possess the properties under study. To achieve the intended goals, the matrix method of weight functions, the matrix method of cutting functions, the matrix method of partial cutting of the author, and the method of integral inequalities of Ya. V. Bykov are developed. Th ...More
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.