二阶非线性振动的Philos型积分平均

数学物理学报 ›› 2012, Vol. 32 ›› Issue (4): 661-669.

二阶非线性振动的Philos型积分平均

林全文¹|俞元洪²

1.广东石油化工学院数学系广东茂名 525000； 2.中国科学院数学与系统科学研究院北京 100190

收稿日期:2010-08-30 修回日期:2011-09-29 出版日期:2012-08-25 发布日期:2012-08-25
基金资助:
广东石油化工学院自然科学研究基金重点课题(LK201002)和国家自然科学研究基金(10971232)资助

Integral Average |of Philos Type for Second Order Nonlinear Oscillation

LIN Quan-Wen¹, YU Yuan-Hong²

1.Department of |Mathematics, Guangdong University |of Petrochemical Technology, Guangdong Maoming 525000; 2.Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190

Received:2010-08-30 Revised:2011-09-29 Online:2012-08-25 Published:2012-08-25
Supported by:
广东石油化工学院自然科学研究基金重点课题(LK201002)和国家自然科学研究基金(10971232)资助

摘要/Abstract

摘要：

研究二阶非线性微分方程
(a(t)x'(t))'+p(t)x'(t)+q(t)f(x(t))=0 (E)

的振动性,在较一般的假设下给出了若干新的振动准则. 该文的方法不同于先前的作者[1--4, 8--10, 13--15], 其结果推广和补充了Philos^[7]和Rogvchenko^[9]早先的结果. 文中也给出了一个说出结果应用的例子.

关键词: 广义Riccati变换, Philos型积分平均, 强次线性, 强超线性, 振动准则

Abstract:

The purpose of this paper is to study the oscillation of second order nonlinear differential equation

(a(t)x'(t))'+p(t)x'(t)+q(t)x(t)=0. (E)
Some new oscillation criteria are established under quite general assumptions. Our methodology is somewhat different from that of previous authors [1--4, 8--10, 13--15]. Our results extend and complement some earlier results of Philos^[7] and Rogovchenko^[9]. An example is also given to illustrate the results.

Key words: Generalized Riccati transformation, Integral average of Philos type, Strongly sublinear, Strongly superlinear, Oscillation criterion

中图分类号:

34C10

林全文, 俞元洪. 二阶非线性振动的Philos型积分平均[J]. 数学物理学报, 2012, 32(4): 661-669.

LIN Quan-Wen, YU Yuan-Hong. Integral Average |of Philos Type for Second Order Nonlinear Oscillation[J]. Acta mathematica scientia,Series A, 2012, 32(4): 661-669.

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