非线性二阶阻尼微分方程的振动定理

数学季刊 ›› 2005, Vol. 20 ›› Issue (1): 1-9.

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非线性二阶阻尼微分方程的振动定理

Department of Mathematics, Tianshui Normal University, Tianshui 741001, China;Department of Mathematics, Lanzhou University, Lanzhou 730000, China

收稿日期:2003-03-03 出版日期:2005-03-30 发布日期:2024-01-24
作者简介:HE Wan-sheng(1956-),male,native of Tianshui,Gansu,a professor of Tianshui Normal Univer- sity,Ph.D.,engages in differential equation.
基金资助:
Several oscillation Supported by the NNSF of China(10071080)；

Oscillation Theorems for Second Order Damped Nonlinear Differential Equations

Department of Mathematics, Tianshui Normal University, Tianshui 741001, China;Department of Mathematics, Lanzhou University, Lanzhou 730000, China

Received:2003-03-03 Online:2005-03-30 Published:2024-01-24
About author:HE Wan-sheng(1956-),male,native of Tianshui,Gansu,a professor of Tianshui Normal Univer- sity,Ph.D.,engages in differential equation.
Supported by:
Several oscillation Supported by the NNSF of China(10071080)；

摘要/Abstract

摘要： Several oscillation criteria are given for the second order nonlinear differential equation with damped term of the form [α(t)(y’(t))^σ]’ +p(t)(y’(t))^σ+ q(t)f(y(t)) = 0, where α∈C(R, (0,∞)), p(t) and q(t) are allowed to change sign on [t₀, ∞), and f∈C¹ (R, R) such that xf(x) > 0 for x ≠0. Our results improve and extend some known oscillation criteria. Examples are inserted to illustrate our results.

关键词: oscillation, second order nonlinear differential equation, damping

Abstract: Several oscillation criteria are given for the second order nonlinear differential equation with damped term of the form [α(t)(y’(t))^σ]’ +p(t)(y’(t))^σ+ q(t)f(y(t)) = 0, where α∈C(R, (0,∞)), p(t) and q(t) are allowed to change sign on [t₀, ∞), and f∈C¹ (R, R) such that xf(x) > 0 for x ≠0. Our results improve and extend some known oscillation criteria. Examples are inserted to illustrate our results.

Key words: oscillation, second order nonlinear differential equation, damping

中图分类号:

O175.29

何万生, 李万同. 非线性二阶阻尼微分方程的振动定理[J]. 数学季刊, 2005, 20(1): 1-9.

HE Wan-sheng, LI Wan-tong . Oscillation Theorems for Second Order Damped Nonlinear Differential Equations[J]. Chinese Quarterly Journal of Mathematics, 2005, 20(1): 1-9.

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非线性二阶阻尼微分方程的振动定理

Oscillation Theorems for Second Order Damped Nonlinear Differential Equations

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