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THE ASYMPTOTIC BEHAVIOR AND OSCILLATION FOR A CLASS OF THIRD-ORDER NONLINEAR DELAY DYNAMIC EQUATIONS
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作者 黄先勇 邓勋环 王其如 《Acta Mathematica Scientia》 SCIE CSCD 2024年第3期925-946,共22页
In this paper,we consider a class of third-order nonlinear delay dynamic equations.First,we establish a Kiguradze-type lemma and some useful estimates.Second,we give a sufficient and necessary condition for the existe... In this paper,we consider a class of third-order nonlinear delay dynamic equations.First,we establish a Kiguradze-type lemma and some useful estimates.Second,we give a sufficient and necessary condition for the existence of eventually positive solutions having upper bounds and tending to zero.Third,we obtain new oscillation criteria by employing the Potzsche chain rule.Then,using the generalized Riccati transformation technique and averaging method,we establish the Philos-type oscillation criteria.Surprisingly,the integral value of the Philos-type oscillation criteria,which guarantees that all unbounded solutions oscillate,is greater than θ_(4)(t_(1),T).The results of Theorem 3.5 and Remark 3.6 are novel.Finally,we offer four examples to illustrate our results. 展开更多
关键词 nonlinear delay dynamic equations nonoscillation asymptotic behavior Philostype oscillation criteria generalized Riccati transformation
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OSCILLATION AND NONOSCILLATION PROPERTIES OF TWO-DIMENSIONAL DELAY DIRECT CONTROL SYSTEMS
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作者 傅予力 《Chinese Science Bulletin》 SCIE EI CAS 1992年第10期870-873,共4页
In a process of control, the oscillation property may influence the property of a system. However, there are very few results about oscillation of control systems.In this note, we consider a delay direct control system:
关键词 DELAY direct control SYSTEMS OSCILLATION PROPERTY nonoscillation PROPERTY
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Nonoscillation for a Second Order Linear Delay Differential Equation with Impulses
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作者 Yan-lingTian Pei-xuanWeng Jin-jiYan 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2004年第1期101-114,共14页
A group of necessary and sufficient conditions for the nonoscillation of a second order linear delay equation with impulses
关键词 nonoscillation impulse linear delay differential equation BOUNDEDNESS
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A NONOSCILLATION RESULT FOR DELAY DIFFERENTIAL EQUATIONS WITH IMPULSES
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作者 申建华 庚建设 《Annals of Differential Equations》 1994年第2期201-207,共7页
Sufficient conditions are obtained for the nonscillation of the impulsive delay differential equation
关键词 IMPULSES Delay differential equations nonoscillations.
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AN OSCILLATION CRITERIA FOR SECOND ORDERFUNCTIONAL EQUATIONS 被引量:14
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作者 申建华 IP. Stavroulakis 《Acta Mathematica Scientia》 SCIE CSCD 2002年第1期56-62,共7页
This paper is concerned with the oscillation of second order linear functional equations of the form x(g(t)) = p(t)x(t) + Q(t)X(g(2)(t)), Where p, Q, g : [t(0), infinity) --> R+ = [0, infinity) are given real value... This paper is concerned with the oscillation of second order linear functional equations of the form x(g(t)) = p(t)x(t) + Q(t)X(g(2)(t)), Where p, Q, g : [t(0), infinity) --> R+ = [0, infinity) are given real valued functions such that g(t) not equivalent to t, lim(t-->infinity) g(t) = infinity. It is proved here that when 0 less than or equal to m := lim inf(t-->infinity) Q(t)P(g(t)) less than or equal to 1/4 all solutions of this equation oscillate if the condition lim(t-->infinity) sup Q(t)P(g(t)) > (1 + root1 -4m/2)(2) (*) is satisfied. It should be emphasized that the condition (*) can not be improved in some sense. 展开更多
关键词 OSCILLATION nonoscillation functional equations
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LINEARIZED OSCILLATIONS FOR AUTONOMOUS DELAY DIFFERENTIAL EQUATIONS
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作者 李永昆 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2000年第7期849-854,共6页
The linearized oscillations of the nonlinear autonomous delay differential equation [GRAPHICS] are studied.
关键词 delay differential equation OSCILLATION nonoscillation
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CONVERGENCE OF SOLUTIONS FOR RLC-NONLINEAR NETWORKS WITH TIME-VARYING ELEMENTS
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作者 蒋断发 程正务 《Acta Mathematica Scientia》 SCIE CSCD 1996年第4期393-405,共13页
This paper studies the asymptotic behavior of solutions for nonlinear RLCnetwoiks which have the following form The function p i,v,t),called tile mired potential function,call be used to construct Liapunov functions t... This paper studies the asymptotic behavior of solutions for nonlinear RLCnetwoiks which have the following form The function p i,v,t),called tile mired potential function,call be used to construct Liapunov functions to prove the convergence of solutions under certain conditiolts. Under the assumption that every element value involving voltage source is asymptotically constallt, we establish four creteria for all solutiolls of such a system to converge to the set of equilibria of its limiting equations via LaSalle invariant principle.We also present two theorems on the existence of periodic solutions for periodically excited uonliltear circuits.This results generalize those of Brayton and Moser[1,2]. 展开更多
关键词 Nonlinear networks nonoscillation and oscillation asymptotic convergence periodic solutions LaSalle invariance principle.
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Oscillatory and Asymptotic Behavior for Second Order Quasilinear Difference Equations
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作者 将建初 李小平 《Northeastern Mathematical Journal》 CSCD 2001年第3期315-322,共8页
This paper is concerned with the oscillatory (and nonoscillatory) behavior of solutions of second oder quasilinear difference equations of the type Some necessary and sufficient conditions are given for the equation t... This paper is concerned with the oscillatory (and nonoscillatory) behavior of solutions of second oder quasilinear difference equations of the type Some necessary and sufficient conditions are given for the equation to admit oscillatory and nonoscillatory solutions with special asymptotic properties. These results generalize and improve some known results. 展开更多
关键词 quasilinear difference equation oscillation and nonoscillation asymptotic behavior
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OSCILLATION OF FIRST ORDER DELAY DIFFERENTIAL EQUATIONS WITH OSCILLATING COEFFICIENTS
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作者 Tang XianhuaDept.ofAppl.Math. CentralSouthUniv.ofTechnology Changsha410083. 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2000年第3期252-258,共7页
In this paper,some sufficient conditions for oscillation of a first order delay differential equation with oscillating coefficients of the formx′(t)+p(t)x(t-τ)=0are established,which improve and generalize some of t... In this paper,some sufficient conditions for oscillation of a first order delay differential equation with oscillating coefficients of the formx′(t)+p(t)x(t-τ)=0are established,which improve and generalize some of the known results in the literature. 展开更多
关键词 Delay differential equation OSCILLATION nonoscillation. This project is supported by the NNSF of China (19831030).
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Asymptotic Behavior of Second Order Neutral Difference Equations with Maxima 被引量:3
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作者 Ethiraju Thandapani 刘召爽 +1 位作者 李巧銮 Sebastian Elizabeth 《Journal of Mathematical Research and Exposition》 CSCD 北大核心 2006年第2期191-198,共8页
The authors consider the following second order neutral difference equation with maxima △(αn△(yn+pnyn-k))-qn max [n-l,n]ys=0,n=0,1,2,…,(*)where {αn}, {pn} and (qn} are sequences of real numbers, and k an... The authors consider the following second order neutral difference equation with maxima △(αn△(yn+pnyn-k))-qn max [n-l,n]ys=0,n=0,1,2,…,(*)where {αn}, {pn} and (qn} are sequences of real numbers, and k and l are integers with k ≥ 1 and l 〉 0. And the asymptotic behavior of nonoscillatory solutions of (*). An example is given to show the difference between the equations with and without "maxima" is studied. 展开更多
关键词 asymptotic behavior nonoscillation neutral difference equation maxima.
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Linearized Oscillation of the First-Order Nonlinear Differential Equation
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作者 李永昆 《Chinese Science Bulletin》 SCIE EI CAS 1994年第23期1937-1942,共6页
1 Introduction and Main Result Kulenovic, Ladas and Meimaridou obtained a result that the
关键词 DELAY EQUATION OSCILLATION nonoscillation.
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Oscillation of High Order Neutral Delay Difference Equations with Continuous Arguments
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作者 Mei HUANG Jian Hua SHEN 《Journal of Mathematical Research and Exposition》 CSCD 2010年第2期374-380,共7页
In this paper, we study oscillation of solutions for a class of high order neutral delay difference equations with variable coefficients -τm [x(t) - c(t)x(t - τ)] = (-1)mp(t)x(t - σ), t ≥ t0 〉 0. Some... In this paper, we study oscillation of solutions for a class of high order neutral delay difference equations with variable coefficients -τm [x(t) - c(t)x(t - τ)] = (-1)mp(t)x(t - σ), t ≥ t0 〉 0. Some sufficient conditions are obtained for bounded oscillation of the solutions. 展开更多
关键词 delay difference equation bounded solution OSCILLATION nonoscillation.
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FORCED OSCILLATION FOR GENERAL DIFFERENTIAL EQUATIONS
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作者 Ravi P. Agarwal Said R. Grace Donal O'Regan 《Annals of Differential Equations》 2007年第1期50-61,共12页
New oscillation criteria for general differential equations of the form x^(n)(t)+pn-1 (t)x^(n-1)(t)+…+P1(t)x′(t)+p0(t)x(t)+q1(t)x^μ (t) = q2 (t)x^λ (t)+e(t) where λ,μ are the ra... New oscillation criteria for general differential equations of the form x^(n)(t)+pn-1 (t)x^(n-1)(t)+…+P1(t)x′(t)+p0(t)x(t)+q1(t)x^μ (t) = q2 (t)x^λ (t)+e(t) where λ,μ are the ratios of positive odd integers, 0 〈 μ 〈 1 and λ 〉 1 are established. 展开更多
关键词 OSCILLATION nonoscillation NONLINEAR COMPARISON
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OSCILLATION OF A CLASS OF SECOND ORDER NEUTRAL DIFFERENCE EQUATIONS WITH CONTINUOUS ARGUMENTS
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作者 Huang Mei(Dept. of Math. and Physics,Hunan First Normal College,Changsha 410002) Shen Jianhua(College of Math. and Computer Science,Hunan Normal University,Changsha 410081) Tang Liang(College of Inform. Administration and Engin.,Jishou University,Zhangjiajie 427000,Hunan) 《Annals of Differential Equations》 2008年第2期150-156,共7页
In this paper,we investigate oscillation of solutions to a class of second order neutral delay difference equations with continuous arguments. We then obtain some sufficient conditions for bounded oscillation of the s... In this paper,we investigate oscillation of solutions to a class of second order neutral delay difference equations with continuous arguments. We then obtain some sufficient conditions for bounded oscillation of the solutions. 展开更多
关键词 neutral difference equation bounded solution OSCILLATION nonoscillation
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OSCILLATION THEOREMS FOR SECOND ORDER NEUTRAL DIFFERENCE EQUATIONS
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作者 Jianmin Guo,Huiqin Chen,Shugui Kang(School of Math.and Computer Sciences,Shanxi Datong University,Datong 037008,Shanxi) 《Annals of Differential Equations》 2012年第3期259-262,共4页
The aim of this paper is to study the oscillation of second order neutral difference equations.Our results are based on the new comparison theorems,that reduce the problem of the oscillation of the second order equati... The aim of this paper is to study the oscillation of second order neutral difference equations.Our results are based on the new comparison theorems,that reduce the problem of the oscillation of the second order equation to that of the first order equation.The comparison principles obtained essentially simplify the examination of the equations. 展开更多
关键词 second order neutral difference equations comparison theorem OSCILLATION nonoscillation
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OSCILLATION CRITERIA FOR ODD-ORDER DELAYED DIFFERENCE EQUATIONS
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作者 Wang Xiaoping 《Annals of Differential Equations》 2007年第4期505-510,共6页
In this paper,we obtain some oscillation criteria to an odd-order delayed difference equation.
关键词 OSCILLATION nonoscillation delay difference equation
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