华东师范大学学报(自然科学版) ›› 2011, Vol. 2011 ›› Issue (5): 73-78.

• 应用数学与基础数学 • 上一篇    下一篇

一类二阶向量中立型阻尼偏微分方程的H-振动性

蔡江涛   

  1. 衡阳师范学院数学与计算科学系, 湖南 衡阳 421008
  • 收稿日期:2010-10-01 修回日期:2011-01-01 出版日期:2011-09-25 发布日期:2011-11-22

H-oscillation of a class of second-order vector neutral partial differential equations with damped terms

CAI Jiang-tao   

  1. Deptartment of Mathematics and Computational Science, Hengyang Normal University, Hengyang Hunan 421008, China
  • Received:2010-10-01 Revised:2011-01-01 Online:2011-09-25 Published:2011-11-22

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摘要： 借助内积降维方法, 利用Riccati变换, 引入参数函数, 将一类具有阻尼项和连续分布滞量的二阶向量中立型偏微分方程的H-振动性问题转化为微分不等式不存在最终正解的问题, 获得了该类方程在Robin边值条件下所有解H-振动的若干充分判据.

关键词: 阻尼, 连续分布滞量, 中立型, 偏微分方程, H-振动性

Abstract: The H-oscillation of a class of second-order vector neutral partial differential equations with damped terms and continuously distributed delays were transformed into the problems of which differential inequalities haven't eventually positive solution by employing the method of reducing dimension with the inner product and making use of Riccati transformation and introducing parameter functions. Some criteria of sufficient conditions for the H-oscillation of all solutions of the equations are obtained under Robin boundary value condition.

Key words: damping, continuously distributed delay, neutral type, partial differential equation, H-oscillation

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