difference equations and other functional equations

... difference equations, ” Acta Applicandae Mathematicae, vol 110, no 3, pp 1277–1287, 2009 S K Ntouyas, Y G Sficas, and P Ch Tsamatos, “Boundary value problems for functional- differential equations, ” ... 1, pp 104–113, 2008 Chinese 11 D J Guo, J X Sun, and Z L Liu, Functional Methods of Nonlinear Ordinary Differential Equations, Shandong Science and Technology Press, Jinan, China, 1995 ... Foundation of Naval Aeronautical and Astronautical University References M J Gai, B Shi, and D C Zhang, “Boundary value problems for second-order singular functional differential equations, ” Chinese Annals...

Ngày tải lên: 21/06/2014, 11:20

... 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, ...

Ngày tải lên: 22/06/2014, 22:20

... difference equations of three and four variables The aim of this paper is to present the generalization of this functional- analytic method for the study of linear and nonlinear partial difference equations ... 238 Functional- analytic method for difference equations nonlinear partial difference equations of two variables, we developed a similar functionalanalytic method in [11, ... 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,...

Ngày tải lên: 23/06/2014, 00:20

... 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,...

Ngày tải lên: 27/01/2014, 03:20

... 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...

Ngày tải lên: 21/06/2014, 05:20

... 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 > ... 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 ... 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

... stability of functional equations see 5–12 Jun and Kim 13 introduced the following cubic functional equation: f 2x y f 2x − y 2f x y 2f x − y 12f x 1.3 and they established the general solution and the ... different functional equations in random normed spaces has been recently studied in 24–29 Recently, Eshaghi Gordji et al 30 established the stability of mixed type cubic and quartic functional equations ... “On the stability of functional equations and a problem of Ulam,” Acta Applicandae Mathematicae, vol 62, no 1, pp 23–130, 2000 12 Th M Rassias, “On the stability of functional equations in Banach...

Ngày tải lên: 22/06/2014, 02:20

... 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 ... Advances in Difference Equations Note that the conditions of Example 2.3 are all satisfied It follows that −1 n β S n −1 n , N 3.5 Now, C2 for which the eigenvalues are λ1 On the other hand, for B S 1S...

Ngày tải lên: 22/06/2014, 11:20

... 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 ... 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) = n =1...

Ngày tải lên: 22/06/2014, 19:20

... Pinto, Convergent solutions of functional difference equations, Journal of Difference Equations and Applications (1998), no 3-4, 277–288 [14] M Migda, A Musielak, and E Schmeidel, On a class of ... Grant Agency, and the Institutional Research Plan AV0Z010190503 References [1] R P Agarwal, Difference Equations and Inequalities Theory, Methods, and Applications, 2nd ed., Monographs and Textbooks ... Theory and Methods (1985), no 2, 171–180 14 BVPs for functional difference equations [9] J R Graef and J Henderson, Double solutions of boundary value problems for 2mth-order differential equations...

Ngày tải lên: 22/06/2014, 22:20

... 10–12, 347–355 [2] 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 ... x ∈ ∂P(θ,b), (1.9) and (i) γ(Tx) > c for x ∈ ∂P(γ,c); (ii) θ(Tx) < b for x ∈ ∂P(θ,b); (iii) α(Tx) > a and P(α,a) = ∅ for x ∈ ∂P(α,a) Then T has at least two fixed points x1 and x2 ∈ P(γ,c) satisfying ... 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),...

Ngày tải lên: 22/06/2014, 22:20

... and asymptotic behavior for abstract retarded functional difference equations in phase space, Journal of Difference Equations and Applications (2002), no 7, 603–640 [12] S Elaydi, S Murakami, and ... theory for such equations (see [15] for discussion and references) Preliminaries and notations Here we explain some notations and the phase space notion As usual, we denote Z, Z+ and Z− the set ... solutions of linear functional 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,...

Ngày tải lên: 22/06/2014, 22:20

... 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 : ... 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 202 of North-Holland Mathematics Studies, ... Doˇ ly and P Reh´ k, “Recessive solution of half-linear second order difference equations, ” Journal s ´ of Difference Equations and Applications, vol 9, no 1, pp 49–61, 2003 14 L H Erbe and B G...

Ngày tải lên: 22/06/2014, 22:20

... 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...

Ngày tải lên: 23/06/2014, 00:20

... 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...

Ngày tải lên: 23/06/2014, 00:20

... 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...

Ngày tải lên: 23/06/2014, 00:20

... 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...

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 R D Driver, G Ladas, and P ... difference equations, and many of them are discrete analogues of differential equations (cf [2, 3, 4, 5, 6, 8, 9, 10, 11, 19]) In recent years, attention has also been given to finite-difference equations ... I), (l) (l) (l) where for each l = 1,2, and n = 1,2, ,γn is positive, and a(l) , bn , and cn are nonnegan tive Lemma 3.1 Let (wn ,zn ) satisfy (3.7), and let (1) (2) a(1) a(2) < γn γn n n (n...

Ngày tải lên: 23/06/2014, 00:20

... 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...

Ngày tải lên: 23/06/2014, 00:20

... recurrences, J Differential Equations 107 (1994), no 2, 238–258 C D Ahlbrandt and A C Peterson, Discrete Hamiltonian Systems Difference Equations, Continued Fractions, and Riccati Equations, Kluwer Texts ... 2000 R P Agarwal and D O’Regan, Infinite Interval Problems for Differential, Difference and Integral Equations, Kluwer Academic Publishers, Dordrecht, 2001 C D Ahlbrandt, Dominant and recessive solutions ... half-linear equations References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] R P Agarwal, Difference Equations and Inequalities, 2nd ed., Monographs and Textbooks in Pure and...

Ngày tải lên: 23/06/2014, 00:20