linear difference equations with discrete transform methods

... control methods for singularly perturbed discrete bilinear systems, Pro[5] ceedings of the 4th Asian Control Conference, Singapore, September 2002, pp 670–675 12 Perturbation method for difference equations ... to the open-loop discrete optimal control problem, Optimal Control Applications & Methods (1982), no 2, 121–131 [15] T Sari and T Zerizer, Perturbations for linear difference equations, Journal ... terms yk , ≤ k ≤ N − n − m, can be computed without any knowledge of the boundary conditions yN −k = βk , ≤ k ≤ m − By analogy with the case of differential equations, we can say that there are m boundary...

Ngày tải lên: 22/06/2014, 22:20

... integrodifferential equations with unbounded delay, and, especially, of linear (non-neutral) integrodifferential equations with unbounded delay Our purpose in this paper is to give the discrete analogues ... 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 ... behaviour of linear functional differential equations, Integral Equations and Operator Theory 47 (2003), no 1, 91–121 [11] J R Graef and C Qian, Asymptotic behavior of forced delay equations with periodic...

Ngày tải lên: 22/06/2014, 22:20

... the fourth section, we present applications to discrete Volterra difference equations with infinite delay During the last few years discrete Volterra equations have emerged vigorously in several ... equivalence for difference equations with infinite delay, Journal of Difference Equations and Applications (1999), no 1, 1–23 [13] J K Hale and J Kato, Phase space for retarded equations with infinite delay, ... Difference Equations and Applications 10 (2004), no 7, 661–689 [17] S Murakami, Representation of solutions of linear functional difference equations in phase space, Nonlinear Analysis Theory, Methods...

Ngày tải lên: 22/06/2014, 22:20

... partial functional differential equations with state-dependent delay, Nonlinear Anal Real World Appl (4) (2006) 510–519 [25] A.V Rezounenko, Differential equations with discrete state-dependent delay: ... space of continuous functions, Nonlinear Anal Ser A: Theory, Methods Appl 70 (11) (2009) 3978–3986 [26] A.V Rezounenko, Non -linear partial differential equations with discrete state-dependent delays ... Inertial manifolds for retarded semilinear parabolic equations, Nonlinear Anal 34 (1998) 907–925 [8] J Wu, Theory and Applications of Partial Functional Differential Equations, Springer-Verlag, New...

Ngày tải lên: 29/10/2015, 14:19

Ngày tải lên: 22/03/2014, 11:20

... obtain the result dealt with in [5] The technique we use in this paper is somewhat similar to one in [1] However, in applying the main idea of Jacob in [1] to the difference equations, we need some ... Basel, 1991, 393 • [5] D Hinrichsen, N.K Son, Stability radii of linear discrete- time systems and symplectic pencils, Int J Robust Nonlinear Control, (1991) 79 [6] A Fischer, J.M.A.M van Neerven, ... stability of delay equations, J Math Analysis Appl., 226(1998) 82 [7] D Hinrichsen, A Ilchmann, A.J Pritchard, Robustness of stability of time-varying linear systems, J Differential Equations, 82(1989)...

Ngày tải lên: 22/03/2014, 11:20

... becomes difference equations with distributed delays without impulses in vector form ∞ μk g (x(m − k)), x(m + 1) = Ax(m) + Bf (x(m)) + C (24) k=1 which contains many popular models such as discrete- time ... systems with aftereffect In: Translations of Mathematical Monographs, vol 157,American Mathematical Society, Providence, RI (1996) 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”...

Ngày tải lên: 21/06/2014, 03:20

... 2.1 Next we consider a nonlinear first-order difference equation 6 Advances in Difference Equations 2.2 The Bound Estimate of a Solution to a Nonlinear First-Order Difference Equation Lemma 2.2 ... Advances in Difference Equations with LN n n−2 ! n n − ! p ρ2 nα2 LN n i N−1 q−p n α1 ρ1 n s N−1 s i and εN n , i 1, 2, being error terms Then εN n , i order linear difference equations i εN n i np ... second-order linear difference equations, ” Journal of Computational and Applied Mathematics, vol 41, no 1-2, pp 65–94, 1992 R Wong and H Li, “Asymptotic expansions for second-order linear difference equations...

Ngày tải lên: 21/06/2014, 11:20

... Regularly Varying Solutions of Half -Linear Difference Equations In this short section we show how the results of Section can be extended to half -linear difference equations of the form Δ Φ Δyk pk ... “Second order linear difference equations and Karamata sequences,” International Journal of Difference Equations, vol 3, no 2, pp 277–288, 2008 V Mari´ , Regular Variation and Differential Equations, ... second order linear difference equations, ” Fasciculi Mathematici, no 31, pp 71–89, 2001 M Cecchi, Z Doˇ l´ , and M Marini, “Positive decreasing solutions of quasi -linear difference sa equations, ”...

Ngày tải lên: 21/06/2014, 11:20

... problem 1.1 and 1.2 with α 0, and λj −K ≤ j ≤ N − 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 Theorem ... in Difference Equations 11 and Proposition 3.6 Assume that k11 > 0, k12 ≤ or k11 ≥ 0, k12 < Equations f λ f λ or −2 hold if and only if λ is a multiple eigenvalue of 1.1 and 1.2 with α or α π ... together with f λ k21 − k22 ψN−1 λ − k12 ΔϕN−1 λ and det K ψN−1 λ k12 , ΔϕN−1 λ k21 − k22 , ΔψN−1 λ k22 Then by Proposition 3.3, λ is a multiple eigenvalue of 1.1 and 1.2 with α 3.34 , together with...

Ngày tải lên: 21/06/2014, 20:20

... Difference Equations this paper is to study the asymptotic behavior of impulsive infinite delay difference equations with continuous variables By establishing an infinite delay difference inequality with ... delay difference equations with continuous variable,” Advances in Difference Equations, vol 2004, no 1, pp 1–10, 2004 G Ladas, “Recent developments in the oscillation of delay difference equations, ” ... nonlinear difference equations with continuous variable,” Journal of Mathematical Analysis and Applications, vol 333, no 2, pp 1203–1215, 2007 Ch G Philos and I K Purnaras, “On non-autonomous linear...

Ngày tải lên: 21/06/2014, 20:20

... half -linear difference sa equations, ” Journal of Difference Equations and Applications, vol 10, no 9, pp 797–808, 2004 16 Advances in Difference Equations 18 O Doˇ ly and S Fiˇ narov´ , “Linearized ... half -linear difference equations, ” Journal of Difference Equations and Applications, vol 7, no 4, pp 483–505, 2001 ˇ a P Reh´ k, “Oscillation and nonoscillation criteria for second order linear ... of half -linear second order difference equations, ” Journal s ´ of Difference Equations and Applications, vol 9, no 1, pp 49–61, 2003 M Cecchi, Z Doˇ l´ , and M Marini, “Nonoscillatory half-linear...

Ngày tải lên: 21/06/2014, 20:20

... 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, ” ... difference equations, ” Computers & c Mathematics with Applications, vol 43, no 6-7, pp 849–867, 2002 15 C A Clark, M R S Kulenovi´ , and J F Selgrade, “On a system of rational difference equations, ” ... Applied Nonlinear Analysis, vol 8, no 1, pp 1–25, 2001 20 Advances in Difference Equations 22 L Gutnik and S Stevi´ , “On the behaviour of the solutions of a second-order difference equation,” c Discrete...

Ngày tải lên: 22/06/2014, 11:20

... 0.87 < 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, ” Journal of Difference Equations and Applications, vol 11, no 9, pp 785–798, 2005 E Liz, “On explicit conditions for the asymptotic stability of linear higher order difference equations, ” ... of 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 Applications,...

Ngày tải lên: 22/06/2014, 11:20

... types of homogeneous linear difference equations with nonconstant coefficients by transforming these equations into homogeneous linear difference equations with constant coefficients over hypergroups This ... functions of the form (i) n → Pn (λ j ) with j = 1,2, ,k and i = 0,1, ,l j − 6 Difference equations on discrete polynomial hypergroups Difference equations with general translation Let us consider ... Difference equations on discrete polynomial hypergroups Much less is known in the case of nonconstant coefficients In this work we offer a method to solve some types of homogeneous linear difference equations...

Ngày tải lên: 22/06/2014, 22:20

... 2 A remark on linear functional equations It is easy to show that H ∈ S The set S with the operation of multiplication ◦ forms a noncommutative ... inverse element to the element Φ in S according to multiplication ◦ in group Ᏻ Linear functional equations of the kth order with constant coefficients Let a j ∈ R, j = 0,1,2, ,k Then the equation ak ... functions are automorphic with respect to any Φ, there are examples of nonconstant automorphic functions One such is p(x) = sin(π(x − n)) on A remark on linear functional equations n ≤ x < n + 1,...

Ngày tải lên: 22/06/2014, 22:20

... differential equations and finite difference equations, Computers & Mathematics with Applications 42 (2001), no 3–5, 695–704 [3] A Cabada, Extremal solutions for the difference φ-Laplacian problem with nonlinear ... conditions, Computers & Mathematics with Applications 42 (2001), no 3–5, 593– 601 [4] J Henderson, Positive solutions for nonlinear difference equations, Nonlinear Studies (1997), no 1, 29–36 [5] ... 2 Positive solutions of difference equations Recently, the existence of positive solutions of finite difference equations with different boundary value conditions is investigated...

Ngày tải lên: 22/06/2014, 22:20

... difference equations with finite delay,” Funkcialaj Ekvacioj, vol 37, no 3, pp 401–413, 1994 [7] S Elaydi and I Gy¨ ri, “Asymptotic theory for delay difference equations, ” Journal of Difference o Equations ... difference equations with infinite delay,” Journal of Difference Equations and Applications, vol 5, no 1, pp 1–23, 1999 [9] I Gy¨ ri and G Ladas, Oscillation Theory of Delay Differential Equations, ... difference equations with unbounded delay,” to appear in Journal of Computational and Applied Mathematics [17] S Zhang, P Liu, and K Gopalsamy, “Almost periodic solutions of nonautonomous linear difference...

Ngày tải lên: 22/06/2014, 22:20

... Oscillation Theory of Linear, Half -Linear, Superlinear and Sublinear Dynamic Equations, Kluwer Academic, Dordrecht, The Netherlands, 2002 ˇ a O Doˇ ly and P Reh´ k, Half -Linear Differential Equations, vol ... a discrete version of the results given in Theorem 3.1 Let p ≥ 2, ck ≥ ck for large k, ∞ Rk ∞, 3.3 and suppose that linear equation 3.1 with R, C given by 1.9 is nonoscillatory Then half -linear ... let linear equation 1.6 be nonoscillatory Then 1.4 is also nonoscillatory ii Let p ∈ 1, and let half -linear equation 1.4 be nonoscillatory Then linear equation 1.6 is also nonoscillatory The linearization...

Ngày tải lên: 22/06/2014, 22:20

... respectively The results in [7, 8] concern difference equations with discrete variable For some related results for difference equations (with discrete variable), see Driver et al [3] and Pituk [13, ... for the case of difference equations with continuous variable In this paper, we give an asymptotic criterion for the solutions of some linear delay difference equations with continuous variable ... properties of linear difference equations with continuous time, Differential Equations Dynam Systems (1993), no 4, 311–324 R D Driver, Some harmless delays, Delay and Functional Differential Equations...

Ngày tải lên: 23/06/2014, 00:20