vector sampled data assignments and vector difference equations
Báo cáo hóa học: "PERIODIC SOLUTIONS OF NONLINEAR VECTOR DIFFERENCE EQUATIONS" ppt
... lemma and the periodicity of F(·,t) and B(·,t) in t M I Gil’ Systems with linear majorants In this section and the next one it is assumed that the norm is ideal That is the vectors z = (zk )n=1 and ... Mechanics and Analysis 12 (1963), 134–149 [8] A Halanay and V Rˇ svan, Stability and Stable Oscillations in Discrete Time Systems, Advances in a Discrete Mathematics and Applications, vol 2, Gordon and ... [1] S S Cheng and G Zhang, Positive periodic solutions of a discrete population model, Functional Differential Equations (2000), no 3-4, 223–230 [2] S Elaydi and S Zhang, Stability and periodicity...
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POWER SERIES TECHNIQUES FOR A SPECIAL SCHRÖDINGER OPERATOR AND RELATED DIFFERENCE EQUATIONS MORITZ docx
... the one hand, if b ≥ −1, this subspace is spanned by y1 On the other hand, if b < −1, it is spanned by y2 M Simon and A Ruffing 117 Remark 4.4 Similar statements hold in the cases (i) and (ii) ... What are the coefficients αk and βk in the cases (i)–(iii)? (i) α0 = 1, αk = for all k ∈ N, and β0 = −B, β1 = d, βk = for all k ∈ N \ {1} (ii) α0 = 1, αk = for all k ∈ N, and β0 = −B, β2 = c, βk = ... b ≥ and b < before!) By Lemma 3.1, we can choose η0 arbitrarily, say η0 ≡ The difference equation (3.3) then yields 114 Power series techniques and Schr¨ dinger operators o η1 = η2 = η3 = and...
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Phương trình vi phân - đại số và phương trình sai phân ẩn = Differential-Algebraic Equations and Implivit Difference Equations
... implicit difference equations, which is sim ilar to that of linear differential-algebraic equations Then we extend this index notion to a class o f nonlinear implicit difference equations and prove ... licit difference equations, Advances ill Difference I'.f/Itaiioiis 2004:3 (2004) 195-200 10 K li Brcium, s L Campbell and L R Pelzold, N u m erical solution < j !\ Ts > ill DAEs, North Holland, ... N II Du and L c L n i, C onnections between im p liiil (lilĨL-iriR X' equations and cli(ÍC lcntiai - algebraic equations A d d M a tli Viet 2(X 1)(2 (M p -6 y I’ K A n h , II T N Yen and T Ọ...
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Sampled Data System and Z-Transform
... is • A ratio of the z-transform of the sampled output and input at the sample instants • A ratio of the z-transform of the output and input when both input and output are trains of pulse • … • ... Process • The z-Transform • Pulse Transfer Function and Manipulation of Block Diagram • Exercises Prior to Lecture • Conventional Control System Sampled data control system The Sampling Process • A ... Pulse Transfer Function Pulse Transfer Function and Manipulation of Block Diagram Open-Loop Systems • Example 1: Figure below shows an open-loop sampled data system Derive the z-transform of the output...
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Tài liệu 02 Ordinary Linear Differential and Difference Equations docx
... Ordinary Linear Differential and Difference Equations 2.1 Differential Equations Classical Solution • Method of Convolution 2.2 Difference Equations Initial Conditions and Iterative Solution • Classical ... y(0+ ) = and y(0+ ) = Setting t = in the above equations and substituting the initial conditions yields c1 + c2 − 15 = − c1 − 2c2 + 45 = and Solution of these equations yields c1 = −8 and c2 = ... 2.25 are yo (0) = and yo (0) = Setting t = in the above ˙ equations and using the initial conditions, we obtain K + K2 = − K1 − 2K2 = and Solution of these equations yields K1 = and K2 = −1 Therefore,...
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Báo cáo hóa học: " Editorial Abstract Differential and Difference Equations" docx
... theory of ordinary and delay differential equations lead to investigations of functional differential equations of various types see the books by Hale and Verduyn Lunel, Wu, and articles by Liang, ... kata, Benchohra, Lizama, Hernandez, etc and the references e e therein On the other hand, the theory of fractional differential equations is also intensively studied and finds numerous applications ... theory developed by J Nunziato, M E Gurtin, and A C Pipkin, the internal energy and the heat flux are described as functionals of u and ux An abstract and more general version of neutral system...
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báo cáo hóa học:" Research Article Solutions and Green’s Functions for Boundary Value Problems of Second-Order Four-Point Functional Difference Equations" ppt
... where ξ, η ∈ 1, T and ξ < η, < τ < T , Δu t u t − u t , Δ2 u t R × Cτ → R is a continuous function, h ∈ Cτ and h t ≥ h ≥ for t ∈ −τ, , α, β, and γ are nonnegative real constants, and r t ≥ for t ... norm · and K is a cone in E For y ∈ K, we have by H1 and the definition of K, max y s t∈ −τ,T max y t y t 3.7 t∈ 1,T For every y ∈ ∂Kp , s ∈ 1, T , and k ∈ −τ, , by the definition of K and 3.5 ... solution if (H4 ) and (H7 ) or (H5 ) and (H8 ) hold Theorem 3.7 Assume that (H1 )–( H3 ) hold Then BVP 3.1 has at least two positive solutions if (H4 ), (H5 ), and (H7 ) or (H4 ), (H5 ), and (H8 ) hold...
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Báo cáo hóa học: " Research Article Global Behavior of Solutions to Two Classes of Second-Order Rational Difference Equations Sukanya Basu and Orlando Meri" docx
... 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 y > qr; ii D2 f x, y if and only if x −r/ p − q , and D2 f x, y > if and only if q − p x > ... 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, ... 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 / m, M Note that...
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Báo cáo hóa học: " Research Article Reducibility and Stability Results for Linear System of Difference Equations" potx
... Lakshmikantham and D Trigiante, Theory of Difference Equations: Numerical Methods and Application, vol 181 of Mathematics in Science and Engineering, Academic Press, Boston, Mass, USA, 1988 S N Elaydi and ... constant regular matrix Then its zero i stable if and only if ρ A ≤ and the eigenvalues of unit modulus are semisimple; ii asymptotically stable if and only if ρ A < 1, where ρ A of A} is the spectral ... ⎡ S −1 0A ρ B < if 2/3 < β < 1, and ρ B if β 2/3 Applying Theorems 3.4 and 3.5, we see that the zero solution of 3.4 is asymptotically stable if 2/3 < β < 1, and is stable if β 2/3 In fact, the...
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Báo cáo hóa học: " Research Article Existence of Periodic and Subharmonic Solutions for Second-Order p-Laplacian Difference Equations" pdf
... Advances in Difference Equations Equations similar in structure to (1.3) arise in the study of the existence of solitary waves of lattice differential equations, see [1] and the references cited ... dimensional Hilbert space and linearly homeomorphic to Rqm On the other hand, we define the norm · p on Eqm as follows: qm x xi p= p 1/ p , (2.5) i=1 for all x ∈ Eqm and p > Clearly, x = x Since ... Since · exist constants C1 , C2 , such that C2 ≥ C1 > 0, and C1 x p ≤ x ≤ C2 x p, p and · ∀x ∈ Eqm are equivalent, there (2.6) P Chen and H Fang Define the functional J on Eqm as follows: qm J(x)...
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Báo cáo hóa học: "Research Article Periodic and Almost Periodic Solutions of Functional Difference Equations with Finite Delay" pdf
... 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 ... [7] S Elaydi and I Gy¨ ri, “Asymptotic theory for delay 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, ... 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, ...
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Báo cáo hóa học: "Research Article Linearized Riccati Technique and (Non-)Oscillation Criteria for Half-Linear Difference Equations" docx
... nonoscillatory, and let xk be its recessive solution Denote by wk rk Φ Δxk / xk and wk rk Φ Δhk /hk the distinguished solutions of the Riccati equations 2.1 and 2.4 , p respectively, and put vk : ... Agarwal, S R Grace, and D O’Regan, 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, ... 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 difference equations, ”...
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ON A CLASS OF FOURTH-ORDER NONLINEAR DIFFERENCE EQUATIONS MAŁGORZATA MIGDA, ANNA MUSIELAK, AND EWA pptx
... linear recurrence equations, Int J Math Math Sci (1984), no 1, 131–149 J R Graef and E Thandapani, Oscillatory and asymptotic behavior of fourth order nonlinear delay difference equations, Fasc ... 1083–1094 E Schmeidel and B Szmanda, Oscillatory and asymptotic behavior of certain difference equation, Nonlinear Anal 47 (2001), no 7, 4731–4742 B Smith and W E Taylor Jr., Oscillatory and asymptotic ... difference equations, Portugal Math 45 (1988), no 1, 105–114 W E Taylor Jr and M Sun, Oscillation properties of nonlinear difference equations, Portugal Math 52 (1995), no 1, 15–24 E Thandapani and I...
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A FUNCTIONAL-ANALYTIC METHOD FOR THE STUDY OF DIFFERENCE EQUATIONS EUGENIA N. PETROPOULOU AND potx
... value problems of partial differential equations, problems of quantum mechanics, and problems of population dynamics and epidemiology (for more details, see [11] and the references therein) Also, ... of I − T exists on H and is uniquely determined and bounded by (I − T)−1 ≤ 1/(1 − T ) In the case of nonlinear equations, we use the following fixed point theorem of Earle and Hamilton [3] Theorem ... characteristic examples of difference equations arising in a problem of mathematics and a problem of physics More precisely, we will establish conditions so that the difference equations under consideration...
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AN ASYMPTOTIC RESULT FOR SOME DELAY DIFFERENCE EQUATIONS WITH CONTINUOUS VARIABLE CH. G. PHILOS AND docx
... 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 and Their Applications ... difference equations, Differential Equations (Colorado Springs, Colo, 1989), Lecture Notes in Pure and Appl Math., vol 127, Dekker, New York, 1991, pp 321–332 G Ladas, L Pakula, and Z Wang, Necessary and ... Ma˘strenko, and E Yu Romanenko, Difference Equations and Their ı Applications, Mathematics and Its Applications, vol 250, Kluwer Academic Publishers, Dordrecht, 1993 J H Shen, Comparison and oscillation...
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MODELLING AIDS EPIDEMIC AND TREATMENT WITH DIFFERENCE EQUATIONS K. M. TAMIZHMANI, A. RAMANI, B. pot
... Kirschner and G F Webb, Understanding drug resistance for monotherapy treatment of HIV infection, Bull Math Biol 59 (1997), no 4, 763–785 A R McLean and C A Michie, In vivo estimates of division and ... step, to discard the negative solution and keep only the physical one, yn > Figures 2.1 and 2.2 show a typical evolution of the discrete model (2.2) The onset and evolution of AIDS epidemic are clearly ... the initial variables x, y, z Since the evolution defined by the equations of system (2.4) involves piecewise linear equations and the max function, one can describe the dynamics of the ultradiscrete...
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PERIODIC SOLUTIONS FOR A COUPLED PAIR OF DELAY DIFFERENCE EQUATIONS GUANG ZHANG, SHUGUI KANG, AND potx
... coupled equations where n ∈ Z We will assume that ω is a positive integer, G and G are double sequences satisfying G(n,s) = G(n + ω,s + ω) and G(n,s) = G(n + ω,s + ω) for n,s ∈ Z, h = {hn }n∈Z and ... continuous functions, and f1 (n + ω,u) = f1 (n,u) as well as f2 (n + ω,u) = f2 (n,u) for any u ∈ R and n ∈ Z By a solution of (1.3), we mean a pair (u,v) of sequences u = {un }n∈Z and v = {vn }n∈Z ... be ω-periodic if un+ω = un and vn+ω = for n ∈ Z Let X be the set of all real ω-periodic sequences of the form u = {un }n∈Z and endowed with the usual linear structure and ordering (i.e., u ≤ v...
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