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Acta Mathematica Sinica,English Series 2003年第4期19卷 801-822页

作者： MengFAN KeWANG PatriciaJ.Y.WONG RaviP.AGARWAL DepartmentofMathematics KeyLaboratoryforVegetationEcologyoftheEducationMinistryofP.R.China NortheastNormalUniversity Changchun130024P.R.China SchoolofElectricalandElectronicEngineering NanyangTechnologicalUniversitySingapore639798Singapore DepartmentofMathematicalSciences FloridaInstituteofTechnologyMelbourneFlorida32901-6975USA

By using the method of coincidence degree and Lyapunov functional, a set ofeasily applicable criteria are established for the global existence and global asymptotic stabilityof strictly positive (componentwise) periodic solution of a periodic n-species Lotka-Volterracompetition system with feedback controls and several deviating arguments. The problem considered inthis paper is in many aspects more general and incorporate as special cases various problems whichhave been studied extensively in the literature. Moreover, our new criteria, which improve andgeneralize some well known results, can be easily checked.

关键词： strictly positive periodic solutions globally asymptotic stability Lotka-Volterra competition system feedback controls deviating arguments coincidence degree Lyapunov functional

EXISTENCE AND UNIQUENESS OF ANTI-PERIODIC SOLUTIONS TO AN nTH-ORDER NONLINEAR DIFFERENTIAL EQUATION WITH MULTIPLE deviating arguments

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Annals of Differential Equations 2012年第1期28卷 105-114页

作者： Jianzhong Xu 1,2,Zongfu Zhou 1 (1.Dept.of Math.,Bozhou Teachers College,Bozhou 236800,Anhui,2.School of Mathematical Sciences,Anhui University,Hefei 230039)

In this paper,we use the Leray-Schauder degree theory to establish some new results on the existence and uniqueness of anti-periodic solutions to an nth-order nonlinear differential equation with multiple deviating ar... 详细信息

关键词： anti-periodic solution Leray-Schauder degree deviating arguments continuation theorem

ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO A CLASS OF HIGHER ORDER NONLINEAR INTEGRO-DIFFERENTIAL EQUATIONS WITH deviating arguments

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Annals of Differential Equations 2009年第2期25卷 208-218页

作者： Jianli Yao (Science School,Shandong Jianzhu University,Ji’nan 250101) Ping Kang (Dept. of Math.,Tianjin Polytechnic University,Tianjin 300160) Fanwei Meng (Dept. of Math.,Qufu Normal University,Qufu 273165,Shandong) Science School Shandong Jianzhu University Ji'nan 250101 Dept. Of Math. Tianjin Polytechnic University Tianjin 300160 Dept. Of Math. Qufu Normal University Qufu P73165 Shandong

In this paper,we study the asymptotic behavior of solutions to a class of higher order nonlinear integro-differential equations with deviating arguments. And some properties of the oscillatory solutions are given. Our... 详细信息

关键词： asymptotic behavior higher order integro-differential equations deviating arguments integro-inequality

Oscillation of Systems of Parabolic Differential Equations with deviating arguments

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Journal of Beijing Institute of Technology 2001年第1期10卷 12-16页

作者：邓立虎王宏洲葛渭高北京理工大学应用数学系北京100081

To study a class of boundary value problems of parabolic differential equations with deviating arguments, averaging technique, Green’s formula and symbol function sign(·) are used. The multi dimensional problem was reduced to a one dimensional oscillation problem for ordinary differential equations or inequalities. Two oscillatory criteria of solutions for systems of parabolic differential equations with deviating arguments are obtained.

关键词： systems of parabolic differential equations boundary value problem deviating arguments oscillation

FORCED OSCILLATION OF SECOND-ORDER NEUTRAL EQUATIONS

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Applied Mathematics and Mechanics(English Edition) 2000年第10期21卷 1197-1200页

作者：王培光葛渭高 Department of Mathematics Hebei University 071002 Baoding P R China Department of Applied Mathematics Beijing Institute of Technology 100081 Beijing P R China

A class of second-order neutral equations with deviating arguments are studied, and sufficient conditions are derived for every solution to be oscillatory.

关键词： oscillation neutral equation deviating arguments

EXISTENCE OF PERIODIC SOLUTIONS TO THIRD-ORDER NONLINEAR DELAY DIFFERENTIAL EQUATION

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Annals of Differential Equations 2011年第4期27卷 409-417页

作者： A.M.A.Abou-El-Ela A.I.Sadek R.O.A.Taie Dept.of Math. Faculty of ScienceAssiut University

By means of the continuation theorem of the coincidence degree theory and analysis techniques,sufficient conditions for the existence of periodic solutions to a kind of third-order neutral delay functional differentia... 详细信息

关键词： periodic solutions coincidence degree deviating arguments thirdorder non-autonomous delay differential equations

New Oscillation Criteria for Second Order Half-Linear Neutral Type Dynamic Equations on Time Scales

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Journal of Applied Mathematics and Physics 2021年第9期9卷 2376-2398页

作者： Faisal Al-Dheleai Elmetwally Elabbasy Department of Mathematics Faculty of Education and Applied Sciences Amran University Amran Yemen Department of Mathematics Faculty of Science Mansoura University Mansoura Egypt

In this paper, we will study the oscillatory properties of the second order half-linear dynamic equations with distributed deviating arguments on time scales. We obtain several new sufficient conditions for the oscillation of all solutions of this equation. Our results not only unify the oscillation of second order nonlinear differential and difference equations but also can be applied to different types of time scales with sup T = ∞. Our results improve and extend some known results in the literature. Examples which dwell upon the importance of our results are also included.

关键词： Dynamic Equation Oscillatory Solutions Neutral deviating arguments

Ruin probabilities with random rates of interest

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Journal of Shanghai University(English Edition) 2006年第3期10卷 211-214页

作者：王汉兴万爱华 Department of Mathematics College of Sciences Shanghai University Shanghai 200444 P. R China Shanghai Lixin University of Commerce Shanghai 200235 P.R. China

A model was proposed for addressing investment risk of the flee reserve in the form of credit or currency risk. This risk was expressed by a constant amount K （ e. g., securitization） upon an interest-increasing event and a random variable Z representing the recovery rate of a bond or a devaluation factor. The model equation is an integro-differential equation with deviating arguments. The analytical solutions were obtained for the probability of survival as Z is a discrete random variable and as Z is a continuous random variable respectively.

关键词： ruin theory credit risk currency risk deviating arguments random rates of interest.