Quadratic Integrability and Boundedness of Solutions of a Class of Linear Nonhomogeneous Differential Equations of Second Order

Consider the nonhomogeneous linear differential equation (r(t)x′ )′＋ p(t)x′＋ [q1(t)＋ q2(t)]x=f(t)(1) By virtue of an auxiliary function with parameters m,n∈ R,we obtain some sufficient conditions under which all solutions of equation (1) belong to L∞ [a,∞ )∩ L2[a,∞ ).Our results improve and generalize some existing theorems.