Asymptotic behaviour of certain second order integro-differential equations

The asymptotic behaviour of certain second order integro-differential equations which are more general than those equations studied in R. P. Agarwal, J. Math. Anal. Appl.86 (1982), 471–475] and S. R. Grace and B. S. Lalli, J. Math. Anal. Appl.76 (1980), 84–90] are discussed. It is pointed out that a defect appeared in the basic Assumption 1 made in both papers, and we avoid this defect in our discussion by using more natural conditions.