AN OSCILLATION CRITERIA FOR SECOND ORDER FUNCTIONAL EQUATIONS

数学物理学报(英文版) ›› 2002, Vol. 22 ›› Issue (1): 56-62.

AN OSCILLATION CRITERIA FOR SECOND ORDER FUNCTIONAL EQUATIONS

申建华, I.P. Stavroulakis

Department of Mathematics, Hunan Normal University, Changsha 410081, China Department of Mathematics, University of Ioannina 451 10, Ioannina, Greece

出版日期:2002-01-14 发布日期:2002-01-14

AN OSCILLATION CRITERIA FOR SECOND ORDER FUNCTIONAL EQUATIONS

SHEN Jian-Hua, I.P. Stavroulakis

Department of Mathematics, Hunan Normal University, Changsha 410081, China Department of Mathematics, University of Ioannina 451 10, Ioannina, Greece

Online:2002-01-14 Published:2002-01-14

摘要/Abstract

摘要：

This paper is concerned with the oscillation of second order linear functional equations of the form x(g(t)) = P(t)x(t) + Q(t)x(g2(t)), where P,Q, g : [t0,∞) → R+ =[0,∞) are given real valued functions such that g(t) 6≡ t, limt!1 g(t) = ∞. It is proved here that when 0 ≤ m := liminft!1 Q(t)P(g(t)) ≤ 1/4 all solutions of this equation oscillate if the condition limsup t!1 Q(t)P(g(t)) > 1 + √1 − 4m 2 2 (∗) is satisfied. It should be emphasized that the condition (∗) can not be improved in some sense.

关键词: Oscillation, nonoscillation, functional equations

Abstract:

Key words: Oscillation, nonoscillation, functional equations

中图分类号:

39B22

申建华, I.P. Stavroulakis. AN OSCILLATION CRITERIA FOR SECOND ORDER FUNCTIONAL EQUATIONS[J]. 数学物理学报(英文版), 2002, 22(1): 56-62.

SHEN Jian-Hua, I.P. Stavroulakis. AN OSCILLATION CRITERIA FOR SECOND ORDER FUNCTIONAL EQUATIONS[J]. Acta mathematica scientia,Series B, 2002, 22(1): 56-62.

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AN OSCILLATION CRITERIA FOR SECOND ORDER FUNCTIONAL EQUATIONS

AN OSCILLATION CRITERIA FOR SECOND ORDER FUNCTIONAL EQUATIONS

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