The behavior of non-oscillatory solutions are shown to be bounded and L^p [0,∞)┤ under the specified conditions, the derivative are shown to be in〖 L〗^2 [0,∞)┤ and the solutions as well as their derivatives shown to approach 0 as t⟶∞ implying stability. We obtain results which extend and complement those known in [1]. Finally, several examples illustrating the usefulness of the procedure are given.