Perturbative Oscillation Criteria and Hardy‐Type Ineqalities

Abstract

Abstract We prove a natural generalization of Kneser's oscillation and Hardy's inequality for Sturm‐Liouville differential expressions. In Particular, assuming − d/dxp 0 (x)+q 0 (x), x ∈ a, b), −∞≦a<b≦∞, to be nonoscillatory near a (or b), we determine condition on q(x) such that − d/dxp 0 (x)+q 0 (x)+q(x) is nonoscillatory, respectively, oscillatory near a (or b)