Journal of South China University of Technology (Natural Science Edition) ›› 2005, Vol. 33 ›› Issue (6): 98-102.

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Oscillation Criteria for the Second-Order Quasi-Linear Diferential Equations with Damping

Jin Chu-hua1  Xu Zhi-ting2  Luo Jiao-wan3   

  1. 1.Faculty of Applied Mathematics,Guangdong Univ.of Tech.,Guangzhou 510090,Guangdong,China;2.College of Mathematics,South China Normal Univ.,Guangzhou 510631,Guangdong,China;3.School of Mathematics and Inform ation Science,Guangzhou Univ.,Guangzhou 510405,Guangdong,China
  • Received:2004-09-24 Online:2005-06-25 Published:2005-06-25
  • Contact: 金楚华(1967-)，男，硕士，讲师，主要从事微分方程理论方面的研究 E-mail:jinchuhua@tom.com
  • About author:金楚华(1967-)，男，硕士，讲师，主要从事微分方程理论方面的研究
  • Supported by:

    国家自然科学青年基金资助项目(10301036)；湖南省杰出青年基金资助项目(04JJ1001)

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Abstract:

W ith the help of Young inequality and HiSld inequality,the oscillatory property of a class of quasi-linear differential equations is investigated by using the Riccati-type transformation and the method of H function.The in-tegral conditions for the oscillation of all the solutions of the equations are also given.Thus,the corresponding re-suits in recent literatures are generalized and improved.By choosing appropriate functions H and Φ ,one can derive
a number of explicit oscillation criteria.Even for the equation without damping,the coresponding results are still different from the form er ones．An example is finally presented to show the validity of the main theorems.

Key words: damping, quasi-linear differential equation, oscillation criterion