Oscillation criteria of second order nonlinear neutral differential equations with damping terms(具阻尼项的二阶非线性中立型微分方程的振动准则)
The purpose of this paper is to establish some new oscillation criteria for the second-order nonlinear neutral differential equations with damping terms which have the form [a(t)z'(t)α-1z'(t)]'+b(t)z'(t)α-1z'(t)+q(t)x(σ(t))β-1x(σ(t))=0， where z(t)=x(t)+p(t)x(τ(t)). Our theor...
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| Format: | Article |
| Language: | zho |
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Zhejiang University Press
2024-01-01
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| Series: | Zhejiang Daxue xuebao. Lixue ban |
| Subjects: | |
| Online Access: | https://doi.org/10.3785/j.issn.1008-9497.2024.01.002 |
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| author | 曾云辉(ZENG Yunhui) 孙文杰(SUN Wenjie) 罗李平(LUO Liping) 俞元洪(YU Yuanhong) |
| author_facet | 曾云辉(ZENG Yunhui) 孙文杰(SUN Wenjie) 罗李平(LUO Liping) 俞元洪(YU Yuanhong) |
| author_sort | 曾云辉(ZENG Yunhui) |
| collection | DOAJ |
| description | The purpose of this paper is to establish some new oscillation criteria for the second-order nonlinear neutral differential equations with damping terms which have the form [a(t)z'(t)α-1z'(t)]'+b(t)z'(t)α-1z'(t)+q(t)x(σ(t))β-1x(σ(t))=0， where z(t)=x(t)+p(t)x(τ(t)). Our theorems improve, extent and unify a number of related results reported in the literature. The wide application of the obtained criteria is illustrated via examples.(建立了二阶非线性中立型阻尼微分方程[a(t)z'(t)α-1z'(t)]'+b(t)z'(t)α-1z'(t)+q(t)x(σ(t))β-1x(σ(t))=0的若干振动准则，其中z(t)=x(t)+p(t)x(τ(t))。改进、推广和统一了已有文献的相关结果，并通过实例说明了所得准则的广泛应用效果。) |
| first_indexed | 2024-04-24T15:35:42Z |
| format | Article |
| id | doaj.art-d7204326e57e4bfd9ea74d6ee788c180 |
| institution | Directory Open Access Journal |
| issn | 1008-9497 |
| language | zho |
| last_indexed | 2024-04-24T15:35:42Z |
| publishDate | 2024-01-01 |
| publisher | Zhejiang University Press |
| record_format | Article |
| series | Zhejiang Daxue xuebao. Lixue ban |
| spelling | doaj.art-d7204326e57e4bfd9ea74d6ee788c1802024-04-02T02:09:53ZzhoZhejiang University PressZhejiang Daxue xuebao. Lixue ban1008-94972024-01-0151151310.3785/j.issn.1008-9497.2024.01.002Oscillation criteria of second order nonlinear neutral differential equations with damping terms(具阻尼项的二阶非线性中立型微分方程的振动准则)曾云辉(ZENG Yunhui)0https://orcid.org/0000-0003-2620-2738孙文杰(SUN Wenjie)1https://orcid.org/0009-0006-0878-7938罗李平(LUO Liping)2俞元洪(YU Yuanhong)31College of Mathematics and Statistics， Hengyang Normal University， Hengyang 421002， Hunan Province， China(1衡阳师范学院 数学与统计学院，湖南 衡阳 421002)2Department of Mathematics and Computational Sciences， Nanyue College of Hengyang Normal University， Hengyang 421008， Hunan Province， China(2衡阳师范学院南岳学院 数学与计算科学系，湖南 衡阳 421008)1College of Mathematics and Statistics， Hengyang Normal University， Hengyang 421002， Hunan Province， China(1衡阳师范学院 数学与统计学院，湖南 衡阳 421002)3Academy of Mathematics and System Science， Chinese Academy of Sciences， Beijing 100190， China(3中国科学院 数学与系统科学研究院, 北京 100190)The purpose of this paper is to establish some new oscillation criteria for the second-order nonlinear neutral differential equations with damping terms which have the form [a(t)z'(t)α-1z'(t)]'+b(t)z'(t)α-1z'(t)+q(t)x(σ(t))β-1x(σ(t))=0， where z(t)=x(t)+p(t)x(τ(t)). Our theorems improve, extent and unify a number of related results reported in the literature. The wide application of the obtained criteria is illustrated via examples.(建立了二阶非线性中立型阻尼微分方程[a(t)z'(t)α-1z'(t)]'+b(t)z'(t)α-1z'(t)+q(t)x(σ(t))β-1x(σ(t))=0的若干振动准则，其中z(t)=x(t)+p(t)x(τ(t))。改进、推广和统一了已有文献的相关结果，并通过实例说明了所得准则的广泛应用效果。)https://doi.org/10.3785/j.issn.1008-9497.2024.01.002oscillation criterion(振动准则)damped equation(阻尼方程)neutral differential equation(中立型微分方程)emden-fowler equation(emden-fowler方程)half-linear differential equation(半线性微分方程) |
| spellingShingle | 曾云辉(ZENG Yunhui) 孙文杰(SUN Wenjie) 罗李平(LUO Liping) 俞元洪(YU Yuanhong) Oscillation criteria of second order nonlinear neutral differential equations with damping terms(具阻尼项的二阶非线性中立型微分方程的振动准则) Zhejiang Daxue xuebao. Lixue ban oscillation criterion(振动准则) damped equation(阻尼方程) neutral differential equation(中立型微分方程) emden-fowler equation(emden-fowler方程) half-linear differential equation(半线性微分方程) |
| title | Oscillation criteria of second order nonlinear neutral differential equations with damping terms(具阻尼项的二阶非线性中立型微分方程的振动准则) |
| title_full | Oscillation criteria of second order nonlinear neutral differential equations with damping terms(具阻尼项的二阶非线性中立型微分方程的振动准则) |
| title_fullStr | Oscillation criteria of second order nonlinear neutral differential equations with damping terms(具阻尼项的二阶非线性中立型微分方程的振动准则) |
| title_full_unstemmed | Oscillation criteria of second order nonlinear neutral differential equations with damping terms(具阻尼项的二阶非线性中立型微分方程的振动准则) |
| title_short | Oscillation criteria of second order nonlinear neutral differential equations with damping terms(具阻尼项的二阶非线性中立型微分方程的振动准则) |
| title_sort | oscillation criteria of second order nonlinear neutral differential equations with damping terms 具阻尼项的二阶非线性中立型微分方程的振动准则 |
| topic | oscillation criterion(振动准则) damped equation(阻尼方程) neutral differential equation(中立型微分方程) emden-fowler equation(emden-fowler方程) half-linear differential equation(半线性微分方程) |
| url | https://doi.org/10.3785/j.issn.1008-9497.2024.01.002 |
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