Title

Necessary and sufficient conditions for the oscillation of a second order linear differential equation

Document Type

Article

Date of Original Version

1-1-2000

Abstract

In this paper we give a necessary and sufficient condition for the oscillation of the second order linear differential equation y″ (t) + p(t) y(t) = 0, t > t0, where p is a locally integrable function and either ∫∞t0 p(t) dt ∈ (-∞, ∞) or ∫∞t [Pn-1 (s)]2 Qn-1(s, t) ds ∈ (-∞, ∞), for some n = 1 , 2 , . . . , where P0(t) = ∫∞t p(s) ds, Pn(t) = ∫∞t Pn-1(s)2 Qn-1 (s, t) ds, Qn-1 (s, t) = exp (∑n-1j=0 ∫st Pj (u) du), n = 1 , 2 , . . . . We give some applications which show how these results unify and imply some classical results in oscillation theory.

Publication Title

Mathematische Nachrichten

Volume

213

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