In theory applications of second order integro-differentialequations, it is crucial to investigate qualitative features of solutionssuch as stability, boundedness, and etc. There is an extensive literature regarding these qualitative behaviors of solutions of second order ordinary differential equations. These qualitative properties ofsolutions of second order ordinary differential equations have beenextensively studied in the literature. Despite this case, the literature on these qualitative aspects of second-order integro-differentialequations is somewhat limited. In this paper, we obtained somenew criteria for the stability and boundedness of solutions to a certain second order nonlinear integro-differential equation (IDE). Bydefining and then using a suitable Lyapunov function (LF), we areable to establish the asymptotic stability and boundedness of solutions of that IDE. In particular cases of the IDE, two examples onthe stability and boundedness of solutions are given. The resultsof this study extend and improve some recent results of the literature and have new contributions to the qualitative theory of IDEs.
Melek Gözen (Wed,) studied this question.
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