Acta mathematica scientia,Series A ›› 2012, Vol. 32 ›› Issue (4): 661-669.

• Articles • Previous Articles     Next Articles

Integral Average |of Philos Type for Second Order Nonlinear Oscillation

 LIN Quan-Wen1, YU Yuan-Hong2   

  1. 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

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

CLC Number: 

  • 34C10
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