Oscillation Criteria for Second-Order Superlinear Neutral Differential Equations

Some oscillation criteria are established for the second-order superlinear neutral differential equations (r(t)|z'(t)|α-1z'(t))'+f(t,x(σ(t)))=0, t≥t0, where z(t)=x(t)+p(t)x(τ(t)), τ(t)≥t, σ(t)≥t, p∈C([t0,∞),[0,p0]), and α≥1. Our results are based on the cases ∫t0∞1/r1/α(t)dt=∞ or ∫t0∞...

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Main Authors: Tongxing Li, Zhenlai Han, Chenghui Zhang, Hua Li
Format: Article
Language:English
Published: Wiley 2011-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2011/367541
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author Tongxing Li
Zhenlai Han
Chenghui Zhang
Hua Li
author_facet Tongxing Li
Zhenlai Han
Chenghui Zhang
Hua Li
author_sort Tongxing Li
collection DOAJ
description Some oscillation criteria are established for the second-order superlinear neutral differential equations (r(t)|z'(t)|α-1z'(t))'+f(t,x(σ(t)))=0, t≥t0, where z(t)=x(t)+p(t)x(τ(t)), τ(t)≥t, σ(t)≥t, p∈C([t0,∞),[0,p0]), and α≥1. Our results are based on the cases ∫t0∞1/r1/α(t)dt=∞ or ∫t0∞1/r1/α(t)dt<∞. Two examples are also provided to illustrate these results.
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series Abstract and Applied Analysis
spelling doaj-art-2c32d71542574c2e8d195b28d8d770df2025-08-20T02:07:38ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/367541367541Oscillation Criteria for Second-Order Superlinear Neutral Differential EquationsTongxing Li0Zhenlai Han1Chenghui Zhang2Hua Li3School of Science, University of Jinan, Jinan, Shandong 250022, ChinaSchool of Science, University of Jinan, Jinan, Shandong 250022, ChinaSchool of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, ChinaSchool of Science, University of Jinan, Jinan, Shandong 250022, ChinaSome oscillation criteria are established for the second-order superlinear neutral differential equations (r(t)|z'(t)|α-1z'(t))'+f(t,x(σ(t)))=0, t≥t0, where z(t)=x(t)+p(t)x(τ(t)), τ(t)≥t, σ(t)≥t, p∈C([t0,∞),[0,p0]), and α≥1. Our results are based on the cases ∫t0∞1/r1/α(t)dt=∞ or ∫t0∞1/r1/α(t)dt<∞. Two examples are also provided to illustrate these results.http://dx.doi.org/10.1155/2011/367541
spellingShingle Tongxing Li
Zhenlai Han
Chenghui Zhang
Hua Li
Oscillation Criteria for Second-Order Superlinear Neutral Differential Equations
Abstract and Applied Analysis
title Oscillation Criteria for Second-Order Superlinear Neutral Differential Equations
title_full Oscillation Criteria for Second-Order Superlinear Neutral Differential Equations
title_fullStr Oscillation Criteria for Second-Order Superlinear Neutral Differential Equations
title_full_unstemmed Oscillation Criteria for Second-Order Superlinear Neutral Differential Equations
title_short Oscillation Criteria for Second-Order Superlinear Neutral Differential Equations
title_sort oscillation criteria for second order superlinear neutral differential equations
url http://dx.doi.org/10.1155/2011/367541
work_keys_str_mv AT tongxingli oscillationcriteriaforsecondordersuperlinearneutraldifferentialequations
AT zhenlaihan oscillationcriteriaforsecondordersuperlinearneutraldifferentialequations
AT chenghuizhang oscillationcriteriaforsecondordersuperlinearneutraldifferentialequations
AT huali oscillationcriteriaforsecondordersuperlinearneutraldifferentialequations