homogeneous linear difference equations with constant coefficients

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... 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 ... found in [1–5]. In particular, we generalize the notions of iterates and linear homogeneous functional equations with constant coefficients. 1.1. Definition of the space S. A function f ∈ C 0 (᏶)belongstoS...

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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 ... compared with the singular perturbation method. We consider a right end perturbation (small parameters are situated on the right), and we deduce the results from Section 2. The comparison with the...

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... motivation of our investigation goes back to [10] dealing with the linear system of differential equations with constant coeffi- cients and constant delay. One of the systems considered has the form ˙ x(t) = ... equa- tions,AdvancesinDifference Equations 2004 (2004), no. 1, 23–36. [13] Ch. G. Philos and I. K. Purnaras, An asymptotic result for some delay difference equations with continuous variable,AdvancesinDifference Equations ... example, in the recent papers [2–9, 11–13]. REPRESENTATION OF SOLUTIONS OF LINEAR DISCRETE SYSTEMS WITH CONSTANT COEFFICIENTS AND PURE DELAY J. DIBL ´ IK AND D. YA. KHUSAINOV Received 16 January...

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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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... the behavior of solutions of linear neutral Volterra difference equations with infinite delay, and, especially, of linear (non-neutral) Volterra difference equations with infinite delay. Our results ... delay difference equations, for the behavior of the solutions of certain linear delay difference equations with continuous var iable as well as for the behavior of solutions of a linear Volterra ... solutions of linear neutral integrodifferential equations with unbounded de- lay, and, especially, of linear (non-neutral) integrodifferential equations with unbounded delay. Our purpose in this paper...

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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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... inhomogeneous second-order linear difference equation; its solution takes the form of a particular solution added to an arbitrary linear combination of solutions to the associated homogeneous linear ... 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, ...

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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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... 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 ... N is even, there exists a constant η 0 >μ N−2 such that fη 0  ≥ 2, which, together with Proposition 3.6, implies that 1.1 and 1.2 with Advances in Difference Equations 17 α  0; α / ...

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... of 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 ... networks difference equation with delays and impulses,” Neural Networks. In press. 11 Q. Zhang, “On a linear delay difference equation with impulses,” Annals of Differential Equations, vol. 18, no. ... impulsive delay difference equations with continuous variables,” Computers & Mathematics with Applications, vol. 55, no. 12, pp. 2732–2739, 2008. Advances in Difference Equations 3 where xtx 1 t,...

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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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... 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, ” ... M. Nurkanovi ´ c, “Asymptotic behavior of a competitive system of linear fractional difference equations, ” Advances in Difference Equations, vol. 2006, Article ID 19756, 13 pages, 2006. 27 M. R....

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... 1. Now let us assume that all coefficients are proportional. Such equations arise as linear approximations of nonlinear difference equations in mathematical biology. Then a straightforward computation ... 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...

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... nonlinear functional boundary conditions, Computers & Mathematics with Applications 42 (2001), no. 3–5, 593– 601. [4] J. Henderson, Positive solutions for nonlinear difference equations, Nonlinear ... equations and finite difference equations, Computers & Mathematics with Applica- tions 42 (2001), no. 3–5, 695–704. [3] A. Cabada, Extremal solutions for the difference φ-Laplacian problem with ... SOLUTIONS OF FUNCTIONAL DIFFERENCE EQUATIONS WITH p-LAPLACIAN OPERATOR CHANG-XIU SONG Received 18 October 2005; Accepted 10 January 2006 The author studies the boundary value problems with p-Laplacian...

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