On Stability and Asymptotic Stability of Solutions for a Linear Fourth Order Volterra Integro-Differential Equation on the Half-Axis

Sufficient conditions for the stability and asymptotic stability of solutions of a linear integro-differential equation of the fourth order of the Volterra type on the semiaxis are established. For this, the following are developed: a non-standard method of reduction to a system, the method of Lyapunov functionals, the method of integro-differential inequalities, the method of integral inequalities, as well as the method of squaring equations, and the Lyusternik-Sobolev lemma is applied. An illustrative example is being built.