linear difference equations with discrete transforms method

... perturbation method applied to the open-loop discrete optimal control problem, Optimal Control Applications & Methods 3 (1982), no. 2, 121–131. [15] T. Sari and T. Zerizer, Perturbations for linear ... convergence of the proposed iterative method. Section 3 is mainly devoted to validate the effectiveness of our method, compared with the singular perturbation method. We consider a right end perturbation ... comparison with the other formal method requires the analysis of its re- sults. We conclude with Section 4. 2. Main result 2.1. Formal asymptotic solution. In this section, we develop a perturbation method...

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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 ... operator. The result is considered as an discrete version of a previous result for time-varying ordinary differential equations [1]. Keywords: Robust stability, Linear difference equation, Input-output ... K d . VNU 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...

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... 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 (x(m − k)) , (24) which contains many popular models such as discrete- time ... 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”...

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... 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, the method ... 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 ... 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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... 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 with discrete variable have attracted considerable attention. In particular, delay effect on the asymptotic behavior and other behaviors of impulsive difference equations with discrete ... 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 ... 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 difference equations, ” Journal of Difference Equations and Applications, vol. 7, no. 4, pp. 483–505, 2001. 5 P. ˇ Reh ´ ak, “Oscillation and nonoscillation criteria for second order linear ... 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...

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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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... and relevant nonlinear equations has been an intensively developed area during the last two decades. Let us compare stability methods for delay differential equations and delay difference equations. ... Many of the methods previously used for differential equations have also been applied to difference equations. However, there are at least two methods which are specific for difference equations. ... 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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... applications. However, linear difference equations with nonconstant coefficients present another im- portant class of di fference equations with much less hig hly developed methods and theo- ries. ... Corporation Advances in Difference Equations Volume 2006, Article ID 51427, Pages 1–10 DOI 10.1155/ADE/2006/51427 6Difference equations on discrete polynomial hypergroups 4. Difference equations with general translation Let ... into hypergroup language and technique, providing effective solution methods for a wide class of linear difference equations with nonconstant coefficients. Copyright © 2006 ´ Agota Orosz. This is...

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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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