linear difference equations with variable coefficients

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... −|ε|/ε 0 , (2.19) with the chosen norm, we obtain (2.5).  3. Comparison with singular perturbation method In this section, we consider a right end perturbation [12]. We are concerned with the boundary ... y (0) k ,0≤ k ≤ N − n − m, can be computed without any knowledge of the boundary conditions y N−k = β k ,0≤ k ≤ m − 1. By analogy with the case of differential equations, we can say that there are m ... & Methods 3 (1982), no. 2, 121–131. [15] T. Sari and T. Zerizer, Perturbations for linear difference equations, Journal of Mathematical Anal- ysis and Applications 305 (2005), no. 1, 43–52. Tahia...

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... ON kTH-ORDER LINEAR FUNCTIONAL EQUATIONS WITH CONSTANT COEFFICIENTS JITKA LAITOCHOV ´ A Received 30 January 2006; Accepted 18 May 2006 Abel functional equations are associated to a linear homogeneous ... functional equation, and linear homogeneous functional equa- tion in S with constant coefficients. T he classical theory of linear homogeneous functional and difference equations is obtained as ... solution of the form f = λ α(x) , (3.3) where α satisfies Abel equation (3.1). Linear system (3.2)isalineardifference equation with constant coefficients of the form a k f (x + k)+a k−1 f (x + k − 1) +...

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... Vietnam Received 10 August 2010 Abstract. This paper deals with a formula of stability radii for an linear difference equation (LDEs for short) with the coefficients varying in time under structured parameter ... Journal of Science, Mathematics - Physics 26 (2010) 175-184 Stability Radii for Difference Equations with Time-varying Coefficients Le Hong Lan* Department of Basic Sciences, University of Transport ... discrete version of a previous result for time-varying ordinary differential equations [1]. Keywords: Robust stability, Linear difference equation, Input-output operator, Stability ra- dius 1. Introduction Many...

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... difference equations, specially, of difference equations with continuous variables. In the recent years, the asymptotic behavior and other behavior of delay difference equations with continuous variables ... cited. 1. Introduction Difference equations with continuous variables are difference equations in which the unknown function is a function of a continuous variable 1. These equations appear as natural ... Difference Equations Volume 2009, Article ID 495972, 13 pages doi:10.1155/2009/495972 Research Article Asymptotic Behavior of Impulsive Infinite Delay Difference Equations with Continuous Variables Zhixia...

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... neutral nonlinear differential equations with delay. Nonlinear Anal. 74(12):3926–3933 (2011). doi:10.1016/j.na.2011.02.029 17. Raffoul, YN: Stability in neutral nonlinear differential equations with ... differential equations with variable delays. Proc Am Math Soc. 136, 909–918 (2008) 19. Ardjouni, A, Djoudi, A: Fixed points and stability in linear neutral differential equations with variable delays. ... stability in differential equations with variable delays. Nonlinear Anal. 63, e233–e242 (2005). doi:10.1016/j.na.2005.02.081 11. Sakthivel, R, Luo, J: Asymptotic stability of nonlinear impulsive stochastic...

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... with aftereffect. In: Translations of Mathematical Monographs, vol. 157,American Mathematical Society, Providence, RI (1996) 2. Xu, DY: Asymptotic behavior of nonlinear difference equations with ... Conclusion In this paper, we consider a class of impulsive difference equations with distributed delays. By establishing an impulsive delay difference inequality and using the properties of “r-cone” ... in terms of Theorem 3.1. Remark 3.3.IfH k (x)=x, then Equation 2 becomes difference equations with distrib- uted delays without impulses in vector form x(m +1)=Ax(m)+Bf (x(m)) + C ∞  k=1 μ k g...

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... in Difference Equations Volume 2010, Article ID 594783, 19 pages doi:10.1155/2010/594783 Research Article Error Bounds for Asymptotic Solutions of Second-Order Linear Difference Equations II: The ... we consider a nonlinear first-order difference equation. 2 Advances in Difference Equations Unlike t he method used by Olver 4 to treat asymptotic solutions of second-order linear differential equations, ... of α i ,ρ i in 1.5, 1.7,and2p − q  1. Equation 3.8 is a second-order linear difference equation with two known linear independent solutions. Its coefficients are quite similar to those in...

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... Regularly Varying Solutions of H alf -Linear Difference Equations In this short section we show how the results of Section 3 can be extended to half -linear difference equations of the form Δ  Φ  Δy k   ... a second-order linear difference equation with arbitrary sign coefficient are established. Relations with the so-called M-classification are also analyzed and a generalization of the results to the half- linear ... order linear difference equations, ” Fasciculi Mathematici, no. 31, pp. 71–89, 2001. 9 M. Cecchi, Z. Do ˇ sl ´ a, and M. Marini, “Positive decreasing solutions of quasi -linear difference equations, ”...

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... 195916, 14 pages doi:10.1155/2010/195916 Research Article Fixed Points and Stability in Nonlinear Equations with Variable Delays Liming Ding, 1, 2 Xiang Li, 1 and Zhixiang Li 1 1 Department of Mathematics ... medium, provided the original work is properly cited. We consider two nonlinear scalar delay differential equations with variable delays and give some new conditions for the boundedness and stability ... 1, pp. 15–32, 2003. 2 B. Zhang, “Fixed points and stability in differential equations with variable delays,” Nonlinear Analysis: Theory, Methods and Applications, vol. 63, no. 5–7, pp. e233–e242,...

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... 1.2 with α  0, and λ j −K0 ≤ j ≤ N −1 denotes the eigenvalue of the problem 1.1 and 1.2 with α  π. We now present the main results of this paper. Advances in Difference Equations 13 linearly ... Corporation Advances in Difference Equations Volume 2009, Article ID 347291, 18 pages doi:10.1155/2009/347291 Research Article Inequalities among Eigenvalues of Second-Order Difference Equations with General Coupled ... 1.2 with α  0 or α  π. If fλ2 or −2 for some λ /  μ k 0 ≤ k ≤ N s ,thenλ is a simple eigenvalue of 1.1 and 1.2 with α  0 or α  π and for every λ /  μ k 0 ≤ k ≤ N s  ,with 2...

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... Difference Equations 18 O. Do ˇ sl ´ y and S. Fi ˇ snarov ´ a, “Linearized Riccati technique and non-oscillation criteria for half -linear difference equations, ” Advances in Difference Equations, ... half -linear second order difference equations, ” Journal of Difference Equations and Applications, vol. 9, no. 1, pp. 49–61, 2003. 8 M. Cecchi, Z. Do ˇ sl ´ a, and M. Marini, “Nonoscillatory half -linear ... of solutions of half -linear difference equations, ” submitted. 10 M. Cecchi, Z. Do ˇ sl ´ a, M. Marini, and I. Vrko ˇ c, “Asymptotic properties for half -linear difference equations, ” Mathematica...

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... stability of a generalized linear neutral stochastic differential equation with variable delays by using the fixed point theory. An asymptotic mean square stability theorem with a necessary and sufficient ... deal with the stability for deterministic differential equations, not for stochastic differential equations. Very recently, Luo 6 studied the mean square asymptotic stability for a class of linear ... asymptotic stability of a generalized linear neutral stochastic differential equation with variable delays by using the fixed point theory. An asymptotic mean square stability theorem with a necessary Meng Wu...

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... Corporation Advances in Difference Equations Volume 2008, Article ID 718408, 21 pages doi:10.1155/2008/718408 Research Article Stability of Equilibrium Points of Fractional Difference Equations with Stochastic ... stochastic linear difference equations, ” Applied Mathematics Letters, vol. 10, no. 3, pp. 111–115, 1997. 47 B. Paternoster and L. Shaikhet, “About stability of nonlinear stochastic difference equations, ” ... equivalent to the stability of the equilibrium point of 2.1. Together with nonlinear equation 2.2 we will consider and its linear part z n1  k  j0 γ j z n−j  σz n ξ n1 ,γ j  a j − b j x λ...

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... Difference Equations and Applications, vol. 1, no. 2, pp. 151–161, 1995. 10 J. S. Yu, “Asymptotic stability for a linear difference equation with variable delay,” Computers & Mathematics with ... of difference equations, ” Functional Differential Equations , vol. 15, no. 3-4, pp. 239–248, 2008. 13 H. Matsunaga, T. Hara, and S. Sakata, “Global attractivity for a nonlinear difference equation with variable ... & Mathematics with Applications, vol. 41, no. 5-6, pp. 543–551, 2001. 14 Y. Muroya, E. Ishiwata, and N. Guglielmi, “Global stability for nonlinear difference equations with variable coefficients,”...

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