continuous variable difference equations with switching and limiter operations

... Kordonis and Philos [7] and Kordonis et al [8], respectively The results in [7, 8] concern difference equations with discrete variable For some related results for difference equations (with discrete variable) , ... 2 Difference equations with continuous variable Philos [11], Kordonis et al [6], and Philos and Purnaras [12] For some related results, we refer to Graef and Qian [5] Moreover, the ... 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 Consider the...

Ngày tải lên: 23/06/2014, 00:20

... Philos and I K Purnaras, “On non-autonomous linear difference equations with continuous variable, ” Journal of Difference Equations and Applications, vol 12, no 7, pp 651–668, 2006 Ch G Philos and ... 679, 2007 J Deng and Z Xu, “Bounded continuous nonoscillatory solutions of second-order nonlinear difference equations with continuous variable, ” Journal of Mathematical Analysis and Applications, ... Dordrecht, The Netherlands, 1993 J Deng, “Existence for continuous nonoscillatory solutions of second-order nonlinear difference equations with continuous variable, ” Mathematical and Computer Modelling,...

Ngày tải lên: 21/06/2014, 20:20

... difference equations, ” Journal of Difference o Equations and Applications, vol 1, no 2, pp 99–116, 1995 [8] S Elaydi, S Murakami, and E Kamiyama, “Asymptotic equivalence for difference equations with ... solution of (3.7) with G(n,φ) = F(n + j∗ ,φ) and with the same δ0 as the one for {u(n)} Set ηn0 − xn0 = μ < δ0 Again, for sufficient large j, we have the similar relations (3.10) and (3.12) with un0 + ... Agarwal, Difference Equations and Inequalities, vol 228 of Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, New York, NY, USA, 2nd edition, 2000 [3] C T H Baker and Y Song, “Periodic...

Ngày tải lên: 22/06/2014, 22:20

... to the difference equations, we need some improvements Many steps of the proofs in the paper [1] are considerably reduced and this reduction is valid not only in discrete case but also in continuous ... set up a formula for stability radius in the space lp and show that when p = and A, E, F are constant matrix, we obtain the result dealt with in [5] The technique we use in this paper is somewhat ... find n0 < m1 < n1 and f1 satisfying f1 = 1, (14) support f1 ⊆ [n0 + 1, m1 ] and ε , L0 (πm1 h) lp(n1 ,∞;Kq ) h lp(0,∞;Ks ) γ 22 Continuing this way, we can find the sequences (fk ) and nk ↑ ∞, nk−1...

Ngày tải lên: 22/03/2014, 11:20

... delay difference equation Appl Math Comput 181, 65–72 (2006) doi:10.1016/j.amc.2006.01.015 Zhu, W: Invariant and attracting sets of impulsive delay difference equations with continuous variables ... (x1 , x2 ) = xi for i = 1, and k = 1, 2, , then Equation 25 becomes difference equation with distributed delays without impulses The parameters of Conditions (A1) and (A3) are as follows: A= ... inequality for stability of impulsive difference equations with distributed delays Journal of Inequalities and Applications 2011 2011:8 Submit your manuscript to a journal and benefit from: Convenient online...

Ngày tải lên: 21/06/2014, 03:20

... recessive and dominant solution holds MB,0 and D i If P and I < ∞, then R MSV ii If P and I MRV MSV ⊂ M∞,0 and D ∞, then R iii If P ∈ 0, 1/4 and I ∞, then R MRV M∞,B MRV ⊂ M∞,0 ⊂ M∞,0 and D MRV ... a S Matucci and P Reh´ k, “Regularly varying sequences and second order difference equations, ” Journal of Difference Equations and Applications, vol 14, no 1, pp 17–30, 2008 J Jaroˇ and T Kusano, ... following result 0, 4.6 ∞ and that M∞,B ⊆ MRV , we Theorem 4.1 For 1.1 , with pk > for large k, the following hold i If P and I < ∞, then M MSV ∪ MRV , with MSV ii If P and I MSV ∪ MRV ∞, then...

Ngày tải lên: 21/06/2014, 11:20

... 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 If f λ or −2 for some λ / μk ≤ k ≤ Ns , then λ is a simple eigenvalue of 1.1 and 1.2 with ... eigenvalue λ0 K < μ0 , 1.1 and 1.2 with α π has only one eigenvalue λ0 −K ≤ μ0 , and 1.1 and 1.2 with α / 0, −π < α < π has only one eigenvalue λ0 K < λ0 eiα K < λ0 −K , and they satisfy ν0 ≤ λ0 ... Publishers, Dordrecht, The Netherlands, 1997 18 Advances in Difference Equations Y Wang and Y Shi, “Eigenvalues of second-order difference equations with periodic and antiperiodic boundary conditions,”...

Ngày tải lên: 21/06/2014, 20:20

... a r ≥ and p > q, b r < and p < q, c r ≥ and p < q, and d r < and p > q We present the proof of case a only, as the proof of the other cases is similar ∈ If r ≥ and p > q, then K1 ∈ m, M and K2 ... is given here without proof Lemma 3.4 Suppose q / p The function f x, y has continuous partial derivatives on L, ∞ , and i D1 f x, y if and only if y qr/ q−p , and D1 f x, y > if and only if p−q ... Difference Equations and Applications, vol 13, no 11, pp 969–1004, 2007 A M Amleh, E Camouzis, and G Ladas, “On second-order rational difference equations II,” Journal of Difference Equations and Applications,...

Ngày tải lên: 21/06/2014, 20:20

... point of 1.1 B Paternoster and L Shaikhet Stochastic perturbations, centering, and linearization—Definitions and auxiliary statements Let {Ω, F, P} be a probability space and let {Fn , n ∈ Z} be ... regions, σ 0.3 Examples Example 4.1 Consider 3.10 with a0 2.9, a1 0.1, b0 b1 0.5 From 1.3 and 1.7 – 1.9 it follows that A 3, B and for any fixed μ and λ such that μ > − 1/4 − λ equation 3.10 has ... obtained by condition 3.3 grey and green regions and by conditions 3.4 , 3.5 cyan and green regions Stability regions obtained via both sufficient conditions of stability 3.3 and 3.4 , 3.5 give together...

Ngày tải lên: 22/06/2014, 11:20

... equation with variable delay,” Computers & Mathematics with Applications, vol 36, no 10–12, pp 203–210, 1998 11 B G Zhang, C J Tian, and P J Y Wong, “Global attractivity of difference equations with variable ... on difference equations with variable delays, and the present paper partially fills up this gap In particular, Theorem 2.18 gives the same stability condition for the equation with variable delays ... Absorption and by the NSERC Research Grant References V L Koci´ and G Ladas, Global Behavior of Nonlinear Difference Equations of Higher Order with c Applications, vol 256 of Mathematics and Its...

Ngày tải lên: 22/06/2014, 11:20

... of (Pε ) exists and is unique and satisfies (2.1) ( j) (0) uniformly for ≤ k ≤ N, where yk and yk are the solutions of (2.2) and (2.4), respectively More precisely, for all n ≥ and all ≤ k ≤ N, ... (ε)) of (3.1) exists and is unique, and satisfies yk (ε) = ∞ j =0 ( j) ε j yk , ≤ k ≤ N, (3.5) ( j) (0) uniformly for ≤ k ≤ N, where yk and yk are the solutions of (2.2) and (2.4), respectively ... difference equations Proof From (3.12) and (3.20), we deduce (0) (− (− (−s+m (0) (0) ys(0) = yt,s + w0,s s) + w1,s s+1) + · · · + wm−1,s −1) = yt,s + ws,s = αs , s = 0,1, ,m − (3.22) Equations (3.10) and...

Ngày tải lên: 22/06/2014, 22:20

... integrodifferential equations with unbounded delay; the results in [21] extend and improve previous ones given by Kordonis and Philos [19] for the special case of (non-neutral) integrodifferential equations with ... Applied Mathematics and Computation 117 (2001), no 2-3, 203–222 , An asymptotic result for some delay difference equations with continuous variable, Ad[29] vances in Difference Equations 2004 (2004), ... solutions of linear neutral Volterra difference equations with infinite delay, and, especially, of linear (non-neutral) Volterra difference equations with infinite delay Our results will be derived...

Ngày tải lên: 22/06/2014, 22:20

... real Banach space, P a cone of X, γ and α two nonnegative increasing continuous maps, θ a nonnegative continuous map, and θ(0) = There are two positive numbers c and M such that γ(x) ≤ θ(x) ≤ α(x), ... R I Avery, C J Chyan, and J Henderson, Twin solutions of boundary value problems for ordinary differential equations and finite difference equations, Computers & Mathematics with Applications 42 ... solutions of difference equations Recently, the existence of positive solutions of finite difference equations with different boundary value conditions is investigated in [1–5] and references therein...

Ngày tải lên: 22/06/2014, 22:20

... difference equations in phase space, Journal of Difference Equations and Applications (2002), no 7, 603–640 [12] S Elaydi, S Murakami, and E Kamiyama, Asymptotic equivalence for difference equations with ... Weighted convergent and bounded solutions of Volterra difference systems with infinite delay, Journal of Difference Equations and Applications (2000), no 4, 461–480 [7] C Cuevas and L Del Campo, An ... difference equations in phase space, Journal of [10] Mathematical Analysis and Applications 277 (2003), no 1, 324–341 C Cuevas and C Vidal 11 [11] C Cuevas and C Vidal, Discrete dichotomies and asymptotic...

Ngày tải lên: 22/06/2014, 22:20

... Therefore |λ j | = with λ j ∈ C\R if and only if c = Now c = and 4c − b2 = − b2 > if and only if c = and −2 < b < Therefore if λ2 + bλ + c = has nonreal roots, and λN = 1, we must have c = and −2 < b ... Im(I − U) and showing that the topological degree of H with respect to Ω and zero is different from zero We will this using a homotopy argument The reader may consult Rouche and Mawhin [13] and the ... constants k1 and k2 and for t ∈ Z+ L will be singular if and only if y(t) = k1 1t + k2 t 1t = k1 + k2 t, (A.8) where y(0) = y(N) and y(1) = y(N + 1) The latter periodicity condition forces k1 and k2...

Ngày tải lên: 23/06/2014, 00:20

... Difference Equations and Inequalities Theory, Methods, and Applications, Monographs and Textbooks in Pure and Applied Mathematics, vol 155, Marcel Dekker, New York, 1992 A M Amleh, J Hoag, and G Ladas, ... relations (A.18) and (A.20) are satisfied From (5.1), (5.3) and arguing as in (A.21) we have that zm ym+1 > D2 /C and 168 Fuzzy max-difference equations so from (5.1), (5.3), and (A.16) it follows ... xn , n = m,m + 1, (2.7) Existence and uniqueness of the positive solutions of fuzzy difference equations (1.1) and (1.2) In this section, we study the existence and the uniqueness of the positive...

Ngày tải lên: 23/06/2014, 00:20

... to the difference equations, we need some improvements Many steps of the proofs in the paper [1] are considerably reduced and this reduction is valid not only in discrete case but also in continuous ... set up a formula for stability radius in the space lp and show that when p = and A, E, F are constant matrix, we obtain the result dealt with in [5] The technique we use in this paper is somewhat ... find n0 < m1 < n1 and f1 satisfying f1 = 1, (14) support f1 ⊆ [n0 + 1, m1 ] and ε , L0 (πm1 h) lp(n1 ,∞;Kq ) h lp(0,∞;Ks ) γ 22 Continuing this way, we can find the sequences (fk ) and nk ↑ ∞, nk−1...

Ngày tải lên: 21/07/2014, 16:21

... the method of upper and lower solutions and the monotone iteration scheme to reaction-diffusion system with discontinuous coefficients and continuous delays and use these methods and the results of ... either to scalar equations without time delays or to coupled system of equations without time delays and with the restrictive conditions that the principal parts are the same and the convection ... x, t, Um−1 , J ∗ Um−1 are continuous in ΩK Then the coefficients of the equations Ll Um In 10 , the estimates near ∂Ω for the equations with continuous coefficients and without time delays are well...

Ngày tải lên: 21/06/2014, 05:20

... “Fixed points and stability in differential equations with variable delays,” Nonlinear Analysis: Theory, Methods and Applications, vol 63, no 5–7, pp e233–e242, 2005 L C Becker and T A Burton, ... : −r, → R there is a continuous solution x t, 0, ψ on an interval 0, T for some T > and Fixed Point Theory and Applications ψ t on −r, Let C S1 , S2 denote the set of all continuous functions ... stable if and only if 1.3 is iii t a h s ds −→ ∞, as t −→ ∞ 1.9 Fixed Point Theory and Applications Theorem 1.3 Burton Suppose that r t r, a constant Let f be odd, increasing on 0, L , and satisfies...

Ngày tải lên: 21/06/2014, 11:20

... points and stability in differential equations with variable delays,” Nonlinear Analysis, vol 63, no 5–7, pp e233–e242, 2005 V B Kolmanovskii and L E Shaikhet, “Matrix Riccati equations and stability ... pp 3679–3687, 2004 T A Burton and T Furumochi, “Fixed points and problems in stability theory for ordinary and functional differential equations, ” Dynamic Systems and Applications, vol 10, no 1, ... c t , e t , q t ∈ C R , R , and τ t , δ t ∈ C R , R with t − τ t → ∞ and t − δ t → ∞ as t → ∞ Here C S1 , S2 denotes the set of all continuous functions φ : S1 → S2 with the supremum norm · In...

Ngày tải lên: 21/06/2014, 23:20