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, e.g., Journal
Mathematische Nachrichten
Volume
213
Citation/Publisher Attribution
Kulenović, M. R., and Ljubović. "Necessary and sufficient conditions for the oscillation of a second order linear differential equation." Mathematische Nachrichten 213, (2000): 105-115. doi: 10.1002/(SICI)1522-2616(200005)213:1<105::AID-MANA105>3.0.CO;2-M.