Full-Text Search:
Home|Journal Papers|About CNKI|User Service|FAQ|Contact Us|中文
《JOURNAL OF MATHEMATICS FOR TECHNOLOGY》 1997-03
Add to Favorite Get Latest Update

Necessary and Sufficient Conditions for Oscillations of Hyperbolic Neutral Partial Differential Equations

Liu Anping Wang Guoqing(China University of Geoscience, Wuhan 430074) Liu Zhongquan(Chongqing Technology Manager College, Chongqing630050)  
In this paper, we investigate oscillatory properties of solutions of certain Hyperbolic neutral partial differential equations and establish a necessary and sufficient condition for oscillations of the equations. The results fully indicate that the oscillations are caused by delay and the oscillatory nature is determined by their characteristic equations. This is one important conclusion and, hence, reveals the essential differences between the equations and those equations without delay.
【Key Words】: hyperbolic neutral delay oscillation.
【CateGory Index】: O175.27
Download(CAJ format) Download(PDF format)
CAJViewer7.0 supports all the CNKI file formats; AdobeReader only supports the PDF format.
【References】
Chinese Journal Full-text Database 10 Hits
1 LIU An-ping 1,YU Wen-hui 1, DING Yan-hong 2 (1.Department of Mathematics & Physics,China University of Geosciences,Wuhan 430074,China; 2.Hubei Taxation School,Wuhan 430064,China);Necessary and sufficient condition for oscillations of nonlinear parabolic partial differential equations[J];Pure and Applied Mathematics;2002-01
2 LIU AnpingLI XingLIU Keying (Dept of Math Phys, China University of Geosciences, Wuhan 430074);Necessary and Sufficient Condition for Oscillations of Delay Hyperbolic Partial Differential Equations[J];Chinese Journal of Engineering Mathematics;2003-04
3 CUI Baotong, LI Weinian (Binzhou Normal College, BinzhouShandong256604);Necessary and Sufficient Conditions for Oscillation of Delay Parabolic Differential Equations with Variable Coefficients[J];JOURNAL OF MATHEMATICS FOR TECHNOLOGY;2000-02
4 LIU An ping (Dept. of Math. & Pbys., China University of Geosciences, Wuhan, Hubei prov. 430074 P.R.China);Sufficient Conditions for Oscillations of Parabolic Partial Differential Equations[J];Journal of Mathematics For Technology;2001-02
5 L IU Zhong- quan1,LIU An- ping2 (1 .Departmentof Basic courses,Chongqing Techenolog Manage College,Chongqing4 0 0 0 50 ; 2 .Departmentof Mathematics and Physics,China University of Geosciences,Wuhan 4 30 0 74 );Oscillations of hyperbolic partial differential equations[J];Journal of Central China Normal University(Natural Sciences);2001-01
6 XIAO Li 1,CUI Chen-pei 1,2 ,YANG Xiang-hui 1 (1.Department of Math. and Phys. China University of Geosciences,Wuhan 430074,China;2.Department of Math.,Luoyang Teachers College,Luoyang 471022,China);Necessary and Sufficient Condition for Oscillations of Parabolic Partial Differential Equations[J];Journal of Luoyang Teachers College;2004-02
7 LIU An-ping, LIU Ke-ying, XUE Qiu-tiao(Department of Mathematics & Physics, China University of Geosciences, Wuhan 430074, China);Oscillations of the Solutions of Nonlinear ParabolicPartial Differential Equations of Neutral Type[J];Mathematics In Practice and Theory;2004-03
8 LU Ping1, CUI Wen-hong2(1.Dept of Mathematic,North china University,Taiyuan 030051,China)(2.Dept of Mathematic,Taiyuan University of Technology,Taiyuan 030024,China);On Oscillation of the Parabolic and Hyperbolic Delay Differential Equations[J];Mathematics in Practice and Theory;2007-21
9 LIU An-ping HE Shui-ming LI Xing (Dept. of Math, and Phys., China University of Geosciences, Wuhan, 430074);NECESSARY AND SUFFICIENT CONDITIONS FOR OSCILLATIONS OF PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS OF NEUTRAL TYPE[J];Journal of Mathematics;2003-03
10 Liu Anping Ou Zhuoling;Necessary and Sufficient Conditions for Oscillations of Hyperbolic Neutral Partial Differential Equation[J];JOURNAL OF WUHAN UNIVERSITY OF TECHNOLOGY;2000-02
【Citations】
Chinese Journal Full-text Database 1 Hits
1 Liu Anping(Chian University of Geosciences, Wuhan 430074);Oscillations of Certain f Hyperbolic Delay Differential Equations with Forced Term[J];JOURNAL OF MATHEMATICS FOR TECHNOLOGY;1996-01
【Co-citations】
Chinese Journal Full-text Database 10 Hits
1 LIU An-ping 1,YU Wen-hui 1, DING Yan-hong 2 (1.Department of Mathematics & Physics,China University of Geosciences,Wuhan 430074,China; 2.Hubei Taxation School,Wuhan 430064,China);Necessary and sufficient condition for oscillations of nonlinear parabolic partial differential equations[J];Pure and Applied Mathematics;2002-01
2 LIU Anping,XIAO Li,LIU Ting,LIU Keying (Dept. of Math. & Phys., China University of Geosciences, Wuhan430074,China);Necessary and sufficient conditions for oscillations of parabolic partial differential equations[J];Pure and Applied Mathematics;2003-03
3 GAO Zheng-hui,LUO Li-ping(Dept.of Mathematics,Hengyang Normal University,Hengyang Hunan,421008);Oscillation of the Solutions of Hyperbolic Partial Differential Equation with Continuous Delay[J];Journal of Chongqing Normal University(Natural Science Edition);2007-01
4 LIU AnpingLI XingLIU Keying (Dept of Math Phys, China University of Geosciences, Wuhan 430074);Necessary and Sufficient Condition for Oscillations of Delay Hyperbolic Partial Differential Equations[J];Chinese Journal of Engineering Mathematics;2003-04
5 LIU An ping (Dept. of Math. & Pbys., China University of Geosciences, Wuhan, Hubei prov. 430074 P.R.China);Sufficient Conditions for Oscillations of Parabolic Partial Differential Equations[J];Journal of Mathematics For Technology;2001-02
6 LIU An-ping, MA Qing-xia, GUO Yan-feng (Department of Mathematics & Physics, China University of Geosciences, Wuhan 430074);Oscillations of the Solutions for Nonlinear Delay Parabolic Partial Differential Equations of Neutral Type[J];College Mathematies;2003-06
7 Liu Anping(Chian University of Geosciences, Wuhan 430074);Oscillations of Certain f Hyperbolic Delay Differential Equations with Forced Term[J];JOURNAL OF MATHEMATICS FOR TECHNOLOGY;1996-01
8 PENG Bai-yu (Mathematics Department,Hengyang Normal University,Hengyang,Hunan,421008,China);Oscillation for a Class of Partial Differential Equations with Continuous Distribution Delay[J];Guangxi Sciences;2007-01
9 GAO Zheng-hui,LUO Li-ping(Dept.of Math.and Comp.Sci.,Hengyang Normal University,Hengyang Hunan 421008,China);Oscillation Criteria for Nonlinear Delay Hyperbolic Partial Functional Differential Equations[J];College Mathematics;2009-06
10 Gong Junxin(Department of Mathematics);OSCILATION THEOREMS OF THE SOLUTION OF A NONLINEAR NEUTRAL PARTIAL DIFFERENTIAL EQUATIONS[J];Journal of Hubei Normal University(Natural Science);1997-06
【Co-references】
Chinese Journal Full-text Database 10 Hits
1 LIU An-ping 1,YU Wen-hui 1, DING Yan-hong 2 (1.Department of Mathematics & Physics,China University of Geosciences,Wuhan 430074,China; 2.Hubei Taxation School,Wuhan 430064,China);Necessary and sufficient condition for oscillations of nonlinear parabolic partial differential equations[J];Pure and Applied Mathematics;2002-01
2 LUO Li-ping~1,OUYANG Zi-gen~2(1.Department of Mathematics,Hengyang Normal University,Hengyang 421008,China;2.Department of Mathematics,Nanhua University,Hengyang 421001,China);Oscillation of Systems of Nonlinear Neutral Hyperbolic Partial Differential Equations with Continuous Distribution Delay[J];Journal of Fujian Normal University(Natural Science Edition);2007-01
3 LIN Wen-xian(School of Mathematics and Information Technology,Hanshan Normal University,Chaozhou 521041,China);Oscillation for Solutions of Systems of Even Order Partial Differential Equations of Neutral Type[J];Journal of Fujian Normal University(Natural Science Edition);2007-01
4 LI Shuyong1,2, MA Zhien1(1faulty of Science, Xi'an Jiaotong University, Xi'an 710049;2Institute of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066);Oscillation on a Population Equation with Diffusion and Delay[J];Chinese Journal of Engineering Mathematics;2003-01
5 Lin Wenxian (Dept. of Math., Hanshan Teacher's College, Chaozhou 521041);OSCILLATION FOR SOLUTIONS OF SYSTEMS OF HIGH ORDER QUASILINEAR PARTIAL DIFFERENTIAL EQUATIONS OF NEUTRAL TYPE[J];Numerical Mathematics A Journal of Chinese Universities;2003-01
6 Zheng Zuxiu (University of Anhui) Ren Hongshan (University of Heilongjiang);Necessary and Sufficient Conditions for Oscillations of Second-order Neutral Equations with First-order Derivative Terms and Several Delays[J];;1994-S1
7 CUI Baotong, LI Weinian (Binzhou Normal College, BinzhouShandong256604);Necessary and Sufficient Conditions for Oscillation of Delay Parabolic Differential Equations with Variable Coefficients[J];JOURNAL OF MATHEMATICS FOR TECHNOLOGY;2000-02
8 Liu Anping(Chian University of Geosciences, Wuhan 430074);Oscillations of Certain f Hyperbolic Delay Differential Equations with Forced Term[J];JOURNAL OF MATHEMATICS FOR TECHNOLOGY;1996-01
9 Li Weinian (Binzhou Normal College, Shandong256604);Necessary and Sufficient Condition for Oscillation of a Neutral Parabolic Equation with Several Delays[J];JOURNAL OF MATHEMATICS FOR TECHNOLOGY;1998-04
10 LUO Li-ping~1,OUYANG Zi-gen~2(1.Dept.of Math.,Hengyang Normal University,Hengyang 421008,China;2.Dept.of Math.,Nanhua University,Hengyang 421001,China);Forced Oscillation of Systems of Nonlinear Neutral Hyperbolic Functional Partial Differential Equations with Continuous Distribution Delay[J];Journal of Henan Normal University(Natural Science);2006-02
【Secondary References】
Chinese Journal Full-text Database 10 Hits
1 LIU An-ping 1,YU Wen-hui 1, DING Yan-hong 2 (1.Department of Mathematics & Physics,China University of Geosciences,Wuhan 430074,China; 2.Hubei Taxation School,Wuhan 430064,China);Necessary and sufficient condition for oscillations of nonlinear parabolic partial differential equations[J];Pure and Applied Mathematics;2002-01
2 LIU Anping,XIAO Li,LIU Ting,LIU Keying (Dept. of Math. & Phys., China University of Geosciences, Wuhan430074,China);Necessary and sufficient conditions for oscillations of parabolic partial differential equations[J];Pure and Applied Mathematics;2003-03
3 GAO Zheng-hui,LUO Li-ping(Dept.of Mathematics,Hengyang Normal University,Hengyang Hunan,421008);Oscillation of the Solutions of Hyperbolic Partial Differential Equation with Continuous Delay[J];Journal of Chongqing Normal University(Natural Science Edition);2007-01
4 ZHU Gang1,2,REN Hong-shan,YU Yuan-hong3(1.Mathematics Science College,Heilongjiang University,Harbin 150080,China;2.Education Science School,Harbin College,Harbin 150086,China;3.Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100080,China);Oscillation criteria for nonlinear neutral hyperbolic equations with continuously distributed delays[J];Journal of Northeast Normal University(Natural Science Edition);2007-02
5 LIU AnpingLI XingLIU Keying (Dept of Math Phys, China University of Geosciences, Wuhan 430074);Necessary and Sufficient Condition for Oscillations of Delay Hyperbolic Partial Differential Equations[J];Chinese Journal of Engineering Mathematics;2003-04
6 LIU An ping (Dept. of Math. & Pbys., China University of Geosciences, Wuhan, Hubei prov. 430074 P.R.China);Sufficient Conditions for Oscillations of Parabolic Partial Differential Equations[J];Journal of Mathematics For Technology;2001-02
7 LIU An-ping, MA Qing-xia, GUO Yan-feng (Department of Mathematics & Physics, China University of Geosciences, Wuhan 430074);Oscillations of the Solutions for Nonlinear Delay Parabolic Partial Differential Equations of Neutral Type[J];College Mathematies;2003-06
8 LUO Li-ping~1,OUYANG Zi-gen~2(1.Dept.of Math.,Hengyang Normal University,Hengyang 421008,China;2.Dept.of Math.,Nanhua University,Hengyang 421001,China);Oscillatory criteria of high-order nonlinear neutral partial differential equations with continuous distribution delay[J];Journal of Lanzhou University of Technology;2006-05
9 PENG Bai-yu(Department of Mathematics,Hengyang Normal University,Hengyang 421008,China);Oscillatory Criteria for a Class of Nonlinear Neutral Partial Differential Equations with Continuous Distribution Delay[J];Journal of Gansu Lianhe University(Natural Science Edition);2007-03
10 LUO Li-ping,YANG Liu (Department of Mathematics and Computational Science,Hengyang Normal University,Hengyang 421008,China);H-oscillation of neutral vector parabolic partial differential equations with continuous deviating arguments[J];Pure and Applied Mathematics;2009-04
【Secondary Citations】
Chinese Journal Full-text Database 1 Hits
1 Liu Anping Yuan Jinchen (China University of Geoseiences);Oscillations of Certain Hyperbolic Delay Differential Equations with Damping Terms[J];;1994-S1
©2006 Tsinghua Tongfang Knowledge Network Technology Co., Ltd.(Beijing)(TTKN) All rights reserved