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The Global Solutions of Impulsive Retarded Functional Differential Equations
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作者 王儒智 孙建安 《Chinese Quarterly Journal of Mathematics》 CSCD 2001年第3期94-99,共6页
In this paper, we present some results on the existence of the golbal solutions of nonlinear impulsive retarded functional differential equations.
关键词 Fréchet spaces Tychonoff fixed point Theorem impulsive retarded functional differential equations
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The Existence of Solutions of Three-point Boundary Value Problems for Second Order Impulsive Differential Equation 被引量:5
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作者 CAI Guo-lan ZHANG Jian-ping GE Wei-gao 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2005年第3期247-257,共11页
We study the existence of solutions to the second order three-point boundary value problem:{x″(t)+f(t,x(t),x′(t))=0,t≠ti,△x(ti)=Ii(x(ti),x′(ti)),i=1,2,…,k,△x′(ti)=Ji(x(ti),x′(t)),i=1... We study the existence of solutions to the second order three-point boundary value problem:{x″(t)+f(t,x(t),x′(t))=0,t≠ti,△x(ti)=Ii(x(ti),x′(ti)),i=1,2,…,k,△x′(ti)=Ji(x(ti),x′(t)),i=1,2,…,k,x(0)=0=x(1)-αx(η),where 0〈η〈1,α∈R,and f:[0,1]×R×R→R,Ii:R×R→R,Ji:R×R→R(i=1,2,…,k)are continuous. Our results is new and different from previous results. In particular, we obtain the Green function of the problem, which makes the problem simpler. 展开更多
关键词 impulsive differential equation boundary value problem fixed points CONE
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CONTINUOUS DEPENDENCE OF THE SOLUTIONS OF IMPULSIVE DIFFERENTIAL EQUATIONS ON THE INITIAL CONDITIONS AND BARRIER CURVES 被引量:2
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作者 K.G.Dishlieva 《Acta Mathematica Scientia》 SCIE CSCD 2012年第3期1035-1052,共18页
The basic objects of investigation in this article are nonlinear impulsive dif- ferential equations. The impulsive moments coincide with the moments of meeting of the integral curve and some of the so-called barrier c... The basic objects of investigation in this article are nonlinear impulsive dif- ferential equations. The impulsive moments coincide with the moments of meeting of the integral curve and some of the so-called barrier curves. For such type of equations, suf- ficient conditions are found under which the solutions are continuously dependent on the perturbations with respect to the initial conditions and barrier curves. The results are applied to a mathematical model of population dynamics. 展开更多
关键词 impulsive differential equations initial condition barrier curves continuous dependence population dynamics
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STABILITY RESULTS OF RANDOM IMPULSIVE SEMILINEAR DIFFERENTIAL EQUATIONS 被引量:2
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作者 M.GOWRISANKAR P.MOHANKUMAR A.VINODKUMAR 《Acta Mathematica Scientia》 SCIE CSCD 2014年第4期1055-1071,共17页
In this paper, we study the existence, uniqueness, continuous dependence, Ulam stabilities and exponential stability of random impulsive semilineax differential equations under sufficient condition. The results are ob... In this paper, we study the existence, uniqueness, continuous dependence, Ulam stabilities and exponential stability of random impulsive semilineax differential equations under sufficient condition. The results are obtained by using the contraction mapping principle. Finally an example is given to illustrate the applications of the abstract results. 展开更多
关键词 semilinear differential equations random impulses stability Hyers-Ulam stability Hyers-Ulam-Rassias stability exponential stability contraction principle
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On the Existence of Positive Solutions for Impulsive Neutral Differential Equations
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作者 何智敏 葛渭高 《Journal of Beijing Institute of Technology》 EI CAS 1999年第4期352-356,共5页
Aim To investigate the existence of positive solutions for impulsive neutral differential equations. Methods The Banach contraction principle was used to establish our results. Results and Conclusion The results of... Aim To investigate the existence of positive solutions for impulsive neutral differential equations. Methods The Banach contraction principle was used to establish our results. Results and Conclusion The results of the existence of positive solutions for impulsive neutral differential equations are obtained. 展开更多
关键词 impulsive neutral differential equation positive solution Banach contraction principle
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NON-INSTANTANEOUS IMPULSIVE FRACTIONAL DIFFERENTIAL EQUATIONS WITH STATE DEPENDENT DELAY AND PRACTICAL STABILITY 被引量:2
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作者 Ravi AGARWAL Ricardo ALMEIDA +1 位作者 Snezhana HRISTOVA Donal O'REGAN 《Acta Mathematica Scientia》 SCIE CSCD 2021年第5期1699-1718,共20页
Nonlinear delay Caputo fractional differential equations with non-instantaneous impulses are studied and we consider the general case of delay,depending on both the time and the state variable.The case when the lower ... Nonlinear delay Caputo fractional differential equations with non-instantaneous impulses are studied and we consider the general case of delay,depending on both the time and the state variable.The case when the lower limit of the Caputo fractional derivative is fixed at the initial time,and the case when the lower limit of the fractional derivative is changed at the end of each interval of action of the impulse are studied.Practical stability properties,based on the modified Razumikhin method are investigated.Several examples are given in this paper to illustrate the results. 展开更多
关键词 non-instantaneous impulses Caputo fractional differential equations practical stability
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Oscillation of Nonlinear Impulsive Delay Hyperbolic Partial Differential Equations 被引量:2
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作者 罗李平 彭白玉 欧阳自根 《Chinese Quarterly Journal of Mathematics》 CSCD 2009年第3期439-444,共6页
In this paper,by making use of the calculous technique and some results of the impulsive differential inequality,oscillatory properties of the solutions of certain nonlinear impulsive delay hyperbolic partial differen... In this paper,by making use of the calculous technique and some results of the impulsive differential inequality,oscillatory properties of the solutions of certain nonlinear impulsive delay hyperbolic partial differential equations with nonlinear diffusion coefficient are investigated.Sufficient conditions for oscillations of such equations are obtained. 展开更多
关键词 NONLINEAR impulsE DELAY hyperbolic partial differential equations OSCILLATION
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Asymptotic stability for impulsive functional differential equations 被引量:1
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作者 罗治国 罗艳 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2009年第10期1317-1324,共8页
In this paper, we investigate the stability of a class of impulsive functional differential equations by using Lyapunov functional and Jensen's inequality. Some new stability theorems are obtained. Examples are given... In this paper, we investigate the stability of a class of impulsive functional differential equations by using Lyapunov functional and Jensen's inequality. Some new stability theorems are obtained. Examples are given to demonstrate the advantage of the obtained results. 展开更多
关键词 STABILITY impulsive functional differential equation Lyapunov functional Jensen's inequality
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Solutions to Boundary Value Problem of Nonlinear Impulsive Differential Equation of Fractional Order 被引量:1
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作者 SU XIN-WEI 《Communications in Mathematical Research》 CSCD 2011年第2期114-126,共13页
This paper is devoted to study the existence and uniqueness of solutions to a boundary value problem of nonlinear fractional differential equation with impulsive effects.The arguments are based upon Schauder and Banac... This paper is devoted to study the existence and uniqueness of solutions to a boundary value problem of nonlinear fractional differential equation with impulsive effects.The arguments are based upon Schauder and Banach fixed-point theorems. We improve and generalize the results presented in[B.Ahmad,S.Sivasundaram, Existence results for nonlinear impulsive hybrid boundary value problems involving fractional differential equations,Nonlinear Analysis:Hybrid Systems,3(2009),251- 258]. 展开更多
关键词 impulsive differential equation boundary value problem fractional derivutive fixed-point theorem
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Numerical Analysis of Balanced Methods for the Impulsive Stochastic Differential Equations 被引量:1
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作者 胡琳 吴强 +2 位作者 徐青翠 张祖锦 李华灿 《Journal of Donghua University(English Edition)》 EI CAS 2015年第4期626-635,共10页
Positive results are proved here about the ability of balanced methods to reproduce the mean square stability of the impulsive stochastic differential equations. It is shown that the balanced methods with strong conve... Positive results are proved here about the ability of balanced methods to reproduce the mean square stability of the impulsive stochastic differential equations. It is shown that the balanced methods with strong convergence can preserve the mean square stability with the sufficiently small stepsize. Weak variants and their mean square stability are also considered. Several numerical experiments are given for illustration and show that the fully implicit methods are superior to those of the explicit methods in terms of mean-square stabilities for relatively large stepsizes especially. 展开更多
关键词 impulsive stochastic differential equation balanced method CONVERGENCE mean square stability
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Asymptotical p-Moment Stability of Stochastic Impulsive Differential Equations and Its Application in Impulsive Control 被引量:1
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作者 牛玉俊 徐伟 李红武 《Communications in Theoretical Physics》 SCIE CAS CSCD 2010年第1期110-114,共5页
In this paper, the asymptotical p-moment stabifity of stochastic impulsive differential equations is studied, and a comparison theory to ensure the asymptotieal p-moment stability for trivial solution of this system i... In this paper, the asymptotical p-moment stabifity of stochastic impulsive differential equations is studied, and a comparison theory to ensure the asymptotieal p-moment stability for trivial solution of this system is established, from which we can find out whether a stochastic impulsive differential system is stable just from a deterministic comparison system. As an application of this theory, we control the chaos of stochastic Chen system using impulsive method, and a stable region is deduced too. Finally, numerical simulations verify the feasibility of our method. 展开更多
关键词 p-moment stability impulsive WHITE-NOISE stochastic differential equations
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MULTIPLE POSITIVE SOLUTIONS FOR FIRST ORDER IMPULSIVE SINGULAR INTEGRO-DIFFERENTIAL EQUATIONS ON THE HALF LINE 被引量:7
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作者 郭大钧 《Acta Mathematica Scientia》 SCIE CSCD 2012年第6期2176-2190,共15页
In this paper, the author discusses the multiple positive solutions for an infinite boundary value problem of first order impulsive singular integro-differential equations on the half line by means of the fixed point ... In this paper, the author discusses the multiple positive solutions for an infinite boundary value problem of first order impulsive singular integro-differential equations on the half line by means of the fixed point theorem of cone expansion and compression with norm type. 展开更多
关键词 impulsive singular integro-differential equation infinite boundary valueproblem fixed point theorem of cone expansion and compression with normtype
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Multiplicity Results for Second Order Impulsive Differential Equations via Variational Methods 被引量:1
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作者 Huanhuan Wang Dan Lu Huiqin Lu 《Engineering(科研)》 2021年第2期82-93,共12页
In this paper we investigate a class of impulsive differential equations with Dirichlet boundary conditions. Firstly, we define new inner product of <img src="Edit_890fce38-e82b-4f36-be40-9d05e8119b88.png"... In this paper we investigate a class of impulsive differential equations with Dirichlet boundary conditions. Firstly, we define new inner product of <img src="Edit_890fce38-e82b-4f36-be40-9d05e8119b88.png" width="40" height="17" alt="" /> and prove that the norm which is deduced by the inner product is equivalent to the usual norm. Secondly, we construct the lower and upper solutions of (1.1). Thirdly, we obtain the existence of a positive solution, a negative solution and a sign-changing solution by using critical point theory and variational methods. Finally, an example is presented to illustrate the application of our main result. 展开更多
关键词 impulsive differential equation Sign-Changing Solution Critical Point Theory Variational Method
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POSITIVE SOLUTION TO FOURTH-ORDER IMPULSIVE DIFFERENTIAL EQUATIONS WITH P-LAPLACIAN 被引量:1
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作者 蔡果兰 葛渭高 《数学物理学报(A辑)》 CSCD 北大核心 2006年第B12期1077-1082,共6页
In order to study three-point BVPs for fourth-order impulsive differential equation of the form with the following boundary conditions u'(0) = u(1) = 0. u'(0) == 0 = u'(1) -φq(α)u'(η). the authors t... In order to study three-point BVPs for fourth-order impulsive differential equation of the form with the following boundary conditions u'(0) = u(1) = 0. u'(0) == 0 = u'(1) -φq(α)u'(η). the authors translate the fourth-order impulsive differential equations with p-Laplacian (*) into three-point BVPs for second-order differential equation without impulses and two-point BVPs for second-order impulsive differential equation by a variable transform. Based on it, existence theorems of positive solutions for the boundary value problems (*) are obtained. 展开更多
关键词 四阶脉冲微分方程 P-拉普拉斯算子 正解 三点边值问题
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MULTIPLE POSITIVE SOLUTIONS FOR FIRST ORDER IMPULSIVE SUPERLINEAR INTEGRO-DIFFERENTIAL EQUATIONS ON THE HALF LINE 被引量:3
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作者 Guo Dajun 《Acta Mathematica Scientia》 SCIE CSCD 2011年第3期1167-1178,共12页
In this paper, the author discusses the multiple positive solutions for an infinite boundary value problem of first order impulsive superlinear integro-differential equations on the half line by means of the fixed poi... In this paper, the author discusses the multiple positive solutions for an infinite boundary value problem of first order impulsive superlinear integro-differential equations on the half line by means of the fixed point theorem of cone expansion and compression with norm type. 展开更多
关键词 impulsive superlinear integro-differential equation infinite boundary value problem fixed point theorem of cone expansion and compression with norm type
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INTEGRATED BISEMIGROUP AND APPLICATIONS TO IMPULSIVE DIFFERENTIALEQUATIONS
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作者 许跟起 《数学物理学报(A辑)》 CSCD 北大核心 1997年第S1期206-210,共5页
In this paper author studies the solvability of abstract hopulsive differential equations on Banach space X. By terms of integrated bisendgroup, author obtains the existence of abstract impulsive differential equation... In this paper author studies the solvability of abstract hopulsive differential equations on Banach space X. By terms of integrated bisendgroup, author obtains the existence of abstract impulsive differential equations with finite contant impulses and gives a condition which makes the impulsive equation be solvable for a Variable impuls. 展开更多
关键词 INTEGRATED bisemigroup impulsive differential equation SOLVABILITY
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THE EXISTENCE OF PERIODIC SOLUTIONS OF IMPULSIVE DIFFERENTIAL EQUATIONS OF MIXED TYPE
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作者 房辉 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2000年第3期291-296,共6页
The existence of periodic solutions for a class of impulsive differential equations of mixed type is studied by constructing periodic sequence solutions of difference equations.
关键词 mixed type impulsive differential equation periodic solution
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Controllability of Second Order Stochastic Impulsive Differential Equations in Hilbert Spaces
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作者 李美丽 田峻钢 李毓媛 《Journal of Donghua University(English Edition)》 EI CAS 2016年第3期375-380,共6页
The exact controllability of second order stochastic impulsive differential equations in Hilbert spaces is studied.By using the Holder's inequality,stochastic analysis and fixed point strategy,some sufficient cond... The exact controllability of second order stochastic impulsive differential equations in Hilbert spaces is studied.By using the Holder's inequality,stochastic analysis and fixed point strategy,some sufficient conditions are given,but no compactness condition is imposed on the cosine family of operators.This work improves some previous results without impulses or stochastic factors. 展开更多
关键词 CONTROLLABILITY stochastic differential equations impulsive differential equations
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Existence of Solutions for Semilinear Impulsive Delay Differential Equations with Nonlocal Conditions
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作者 李美丽 刘海强 《Journal of Donghua University(English Edition)》 EI CAS 2010年第5期614-617,共4页
In this paper,by using Schaefer fixed-point theorem,the existence of mild solutions of semilinear impulsive delay differential equations with nonlocal conditions is studied.The results obtained are a generalization an... In this paper,by using Schaefer fixed-point theorem,the existence of mild solutions of semilinear impulsive delay differential equations with nonlocal conditions is studied.The results obtained are a generalization and continuation of the recent results on this issue.In the end,an example is given to show the application of the results. 展开更多
关键词 impulsive delay differential equations nonlocal conditions mild solution Schaefer fixed-point theorem
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ON DETERMINATION OF THE IMPULSIVE SOLUTIONS AND IMPULSIVE PROPERTIES TO LINEAR NON-HOMOGENEOUS MATRIX DIFFERENTIAL EQUATIONS
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作者 Tan Liansheng 《Acta Mathematica Scientia》 SCIE CSCD 2000年第2期261-272,共12页
This note contains three main results.Firstly,a complete solution of the Linear Non-Homogeneous Matrix Differential Equations(LNHMDEs)is presented that takes into account both the non-zero initial conditions of the ps... This note contains three main results.Firstly,a complete solution of the Linear Non-Homogeneous Matrix Differential Equations(LNHMDEs)is presented that takes into account both the non-zero initial conditions of the pseudo state and the nonzero initial conditions of the input.Secondly,in order to characterise the dynamics of the LNHMDEs correctly,some important concepts such as the state,slow state(smooth state)and fast state(impulsive state)are generalized to the LNHMDE case and the solution of the LNHMDEs is separated into the smooth(slow)response and the fast(implusive)response.As a third result,a new characterization of the impulsive free initial conditions of the LNHMDEs is given. 展开更多
关键词 linear matrix differential equation impulsive and smooth solution impulsive free initial conditions {1}-inverse
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