Asymptotic Behavior and L 2- Properties of Non- Oscillatory Solutions to x”+a(t)x’+b(t)x=0

Abstract. In this note, sufficient conditions are given to guarantee when all solutions to the linear homogeneous differential equation x”+a(t)x’+b(t)x=0 are both bounded and elements in L 2[0,∞). Furthermore, when the solutions are non-oscillatory, they are shown to approach 0 as t→∞