带有阻尼项的四阶微分方程的振动性  

Oscillation of Fourth-Order Differential Equation with Damping Term

作　　者：贾对红[1] JIA Dui-hong(Department of Mathematics,Changzhi University,Changzhi 046000,China)

机构地区：[1]长治学院数学系,山西长治046000

出　　处：《数学的实践与认识》2020年第21期278-285,共8页Mathematics in Practice and Theory

基　　金：长治学院教学改革创新项目(JC201911);长治学院校级基金项目(XJ2020001301);山西省高等学校教学改革创新项目(J2018180)。

摘　　要：高阶微分方程解的振动性问题近年来被广泛关注并取得了许多优秀成果,主要研究了一类带有阻尼项的四阶微分方程的解的振动性,应用Riccati积分变换得到了不同条件下方程解的振动性并给出了几个振动准则,推广了已有文献的结果,最后用例子作了验证.In recent years,the oscillation of solutions of higher order differential equations has been widely concerned and many excellent results have been obtained.In this paper,we mainly study the oscillation of solutions of a class of fourth order differential equations with damping terms.By using Riccati integral transformation,we obtain the oscillation of solutions of the equations under different conditions and give several oscillation criteria,which generalize the results of the existing literature.Finally,an example is used to verify it.

关 键 词：四阶 微分方程 RICCATI变换 阻尼项 

分 类 号：O175[理学—数学]