linear difference equations ppt

... Solutions and Green’s Functions for Boundary Value Problems of Second-Order Four-Point Functional Difference Equations Yang Shujie and Shi Bao Institute of Systems Science and Mathematics, Naval Aeronautical ... functionaldifferential equations,” Chinese Annals of Mathematics, vol 23A, no 6, pp 1–10, 2001 Chinese. 2 Y Guo and J Tian, “Two positive solutions for second-order quasilinear differential equation ... changing nonlinearities,” Journal of Computational and Applied Mathematics, vol 169, no 2, pp 345–357, 2004. 3 J Henderson and A Peterson, “Boundary value problems for functional difference equations,”

Ngày tải lên: 21/06/2014, 11:20

... pagesdoi:10.1155/2009/521058 Research Article Summation Characterization of the Recessive Solution for Half-Linear Difference Equations Ondˇrej Do ˇsl ´y1 and Simona Fi ˇsnarov ´a2 1 Department of Mathematics and ... certain nonlinear function which appears in the Picone-type identity for1.1 The recessive solution of1.1 is a discrete counterpart of the concept of the principal solution of the half-linear ... medium, provided the original work is properly cited 1 Introduction We consider the second-order half-linear difference equation Δr k ΦΔx k   c k Φx k1   0, Φx : |x| p−2 x, p > 1, 1.1

Ngày tải lên: 21/06/2014, 20:20

... Trang 1EQUATIONS WITH SMALL PARAMETERSTAHIA ZERIZER Received 14 December 2005; Revised 5 April 2006; Accepted 26 April 2006 We consider a boundary value problem for a linear difference ... equating the coefficients at the same powers ofε, a set of equations is obtained For the zeroth-order asymptotic approximation, the resulting equations are given by y(0) k = α k, k =0, 1, ,n −1, a ... multi-time-scale digital systems Such systems are Hindawi Publishing Corporation Advances in Di fference Equations Volume 2006, Article ID 19214, Pages 1 12 DOI 10.1155/ADE/2006/19214 Trang 2prevalent

Ngày tải lên: 22/06/2014, 22:20

... Trang 1NONLINEAR DIFFERENCE EQUATIONSRAVI P AGARWAL, SAID R GRACE, AND TIM SMITH Received 11 August 2005; Revised 20 ... 2006; Accepted 25 April 2006 Some new criteria for the oscillation of first-order forced nonlinear difference equations of the formΔx(n) + q1(n)x μ(n + 1) = q2(n)x λ(n + 1) + e(n), where λ,μ are the ... provided the original work is properly cited 1 Introduction We consider first-order forced nonlinear difference equations of the type Δx(n) + p(n)x(n + 1) + q1(n)x μ(n + 1) = e(n), (1.1) Δx(n) = q2(n)x

Ngày tải lên: 22/06/2014, 22:20

... 1fference EquationsVolume 2008, Article ID 438130, 18 pages doi:10.1155/2008/438130 Research Article Linearized Riccati Technique and (Non-)Oscillation Criteria for Half-Linear Difference Equations ... i Let p ≥ 2 and let linear equation 1.6 be nonoscillatory Then 1.4 is also nonoscillatory. 1.4 be nonoscillatory Then linear equation 1.6 is also nonoscillatory. The linearization technique ... deeply developed linear oscillation theory when investi-gating oscillations of half-linear equation1.1 As we will see in the next sections, compared to the continuous case, the linearization technique

Ngày tải lên: 22/06/2014, 22:20

... of infinity,” like in the linear case Other asymptotic properties of recessive and dominant solutions are treated too 1 Introduction Consider the second-order half-linear difference equation ∆
a ... Another concept recently extended to the half-linear case is the concept of a reces-sive solution (see [11]) We recall (see, e.g., [1,8,14]) that in the linear case, if (1.2) is nonoscillatory, then ... (1.2), linearly independent of u Solution u is called a recessive solution and x a dominant solution Both solutions play Copyright©2005 Hindawi Publishing Corporation Advances in Di fference Equations

Ngày tải lên: 23/06/2014, 00:20

... 1FOR HIGHER-ORDER MONOTONE DIFFERENCE EQUATIONSEDUARDO LIZ AND MIH ´ALY PITUK Received 21 May 2004 Asymptotic estimates are established for higher-order scalar difference equations and in-equalities ... i+g
n,xn,xn −1, ,xn − r Trang 3under the assumption that its linear partyn+1 = k  i =0 generates a monotone system and the growth of the nonlinearity g : N × R r+1 → R is controlled by a positively ... 3.7is linear, then the value of the limit (3.12) can be given explicitly in terms of the initial data (x0,x −1, ,x − k) (see [2] or [4] for details) The proof ofTheorem 3.7will be based on a nonlinear

Ngày tải lên: 23/06/2014, 00:20

... permits to transform the nonlinear problem into a linear one Regarding the class of linear multistep meth-ods (LMMs), the propagation of the errors can be studied by means of a linear difference equation ... mentioned in the Introduction, the study of the stability for dissipative nonlinear problems is made by linearizing the nonlinearity around the asymptotically stable critical point This is equivalent ... October 2004 The study of the stability properties of numerical methods leads to considering linear dif-ference equations depending on a complex parameterq Essentially, the associated char-acteristic

Ngày tải lên: 23/06/2014, 00:20

... these equations are not adjoint equations and are referred to as quasi-adjoint equations. Equation (E) is a special case of linearnth-order difference equations with quasi-differ-ences Such equations ... above-quoted results for third-order differential equations Moreover, the oscillation of (E) and (EA) is characterized by means of second-order linear difference equations and the problem of the number ... Trang 1INVOLVING QUASI-DIFFERENCESZUZANA DOˇSL ´A AND ALEˇS KOBZA Received 30 June 2004; Revised 20 September 2004; Accepted 12 October 2004 We study the third-order linear difference equation

Ngày tải lên: 23/06/2014, 00:20

... SCIENCE Ngô Thi Thanh Nga STABILITY AND ROBUST STABILITY OF SINGULAR LINEAR DIFFERENCE EQUATIONS Speciality: Dierential and Integral Equations Speciality Code: 62 46 01 03 THESIS FOR THE DEGREE OFDOCTOR ... some fundamental notions on singular lineardierence equations and other auxiliary results which will be used in nextchapters 1.1 Linear singular dierence equations by tractability-index approach ... 10Chapter 2 Singular systems of rst-order dierence equations 282.1 Stability notions for singular dierence equations 28 2.2 Stability of perturbed equations 32 2.2.1 The case of one-sided perturbation

Ngày tải lên: 15/09/2020, 06:59

... SCIENCE Ngô Thi Thanh Nga STABILITY AND ROBUST STABILITY OF SINGULAR LINEAR DIFFERENCE EQUATIONS Speciality: Dierential and Integral Equations Speciality Code: 62 46 01 03 THESIS FOR THE DEGREE OFDOCTOR ... some fundamental notions on singular lineardierence equations and other auxiliary results which will be used in nextchapters 1.1 Linear singular dierence equations by tractability-index approach ... 10Chapter 2 Singular systems of rst-order dierence equations 282.1 Stability notions for singular dierence equations 28 2.2 Stability of perturbed equations 32 2.2.1 The case of one-sided perturbation

Ngày tải lên: 03/07/2021, 10:36

... Issue-6; Jun, 2022INVERSE OF THE GENERALIZED VANDERMONDE MATRIX VIA THE FUNDAMENTAL SYSTEM OF LINEAR DIFFERENCE EQUATIONS CLAUDEMIR ANIZ AND MUSTAPHA RACHIDI Instituto de Matem´atica INMA, UFMS, Av Costa ... Van-dermonde matrix, using the analytic properties of a fundamental system related to a specific linear difference equations We establish two approaches allowing us to provide explicit formulas for the ... Words: Generalized Vandermonde matrix; Inverse of the generalized Vander-monde matrix; Linear difference equations; Analytic formulas; Fibonacci funda-mental system. 2010 Mathematical Subject

Ngày tải lên: 11/10/2022, 16:50

... time is usually deseribed by differential and difference equations In discrete-time scale, mathematical modcls lead to difference equations Difference equations play imporlani roles in many areas ... definitions 21 1.2.3 Linear time-invariant singular difference equations af sec- 1.3 Further auxiliary resulis cuc ee 28 Trang 10Chapter 2 Singular systems of first-order difference equations 28 ... Ngô Thị Thanh Nga STABILITY AND ROBUST STABILITY OF SINGULAR LINEAR DIFFERENCE EQUATIONS Speciality: Differential and Integral Equations Speciality Code: 62 46 01 03 THESIS FOR THE DEGREE

Ngày tải lên: 15/05/2025, 21:50

... is dominant if and only if∞ ka1/y k y k1  < ∞. 3 Regularly Varying Solutions of Linear Difference Equations In this section we prove conditions guaranteeing that1.1 has regularly varying ... second-order linear difference equation with arbitrary sign coefficient are established Relations with the so-calledM-classification are also analyzed and a generalization of the results to the half-linear ... approach At the same time, our results can be seen as a discrete counterpart to the ones for linear differential equations, see, for example, 2 also examine relations with the so-calledM-classification

Ngày tải lên: 21/06/2014, 11:20

... Trang 1fference EquationsVolume 2008, Article ID 932831, 22 pages doi:10.1155/2008/932831 Research Article Asymptotic Representation of the Solutions of Linear Volterra Difference Equations Istv ... the asymptotic behaviour of solutions of linear Volterra difference equations Some sufficient conditions are presented under which the solutions to a general linear equation converge to limits, which ... solutions of Volterra difference equations isextensive, and application of this theory is rapidly increasing to various fields For the basictheory of difference equations, we choose to refer to

Ngày tải lên: 22/06/2014, 11:20

... Trang 1fference EquationsVolume 2007, Article ID 96415, 12 pages doi:10.1155/2007/96415 Research Article Unbounded Perturbations of Nonlinear Second-Order Difference Equations at Resonance ... solutions of nonlinear discrete boundary value problems Δ2u(t −1) +μ1u(t) + g(t,u(t)) = h(t), t ∈ T,u(a) = u(b + 2) =0, whereT:= { a + 1, , b + 1 },h : T → R,μ1is the first eigenvalue of the linear problemΔ2u(t ... eigenvalue is one dimen-sional The following lemma is crucial to the study of nonlinear perturbations of the linear problem (1.1) The required results are somewhat scattered in [1, Chapters 6-7]

Ngày tải lên: 22/06/2014, 19:20

... two dimensional linear fractional c c system of difference equations,... and J F Selgrade, On a system of rational difference equations, c Journal of Difference Equations and Applications ... ASYMPTOTIC BEHAVIOR OF A COMPETITIVE SYSTEM OF LINEAR FRACTIONAL DIFFERENCE EQUATIONS M. R. S. KULENOVI ´ C AND M. NURKANOVI ´ C Received 18 July 2005; Revised ... Perron’s theorems for difference equations, Journal of Difference e Equations and... Clark and M R S Kulenovi´ , A coupled system of rational difference equations, Computers & c Mathematics

Ngày tải lên: 22/06/2014, 22:20

... difference equations, for the behavior investiga-of the solutions investiga-of certain linear delay difference equations with continuous variable aswell as for the behavior of solutions of a linear ... study the behavior of solutions of linear neutral Volterra difference equationswith infinite delay, and, especially, of linear (non-neutral) Volterra difference equationswith infinite delay Our results ... of solutions of linear neutral integrodifferential equations with unbounded de-lay, and, especially, of linear (non-neutral) integrodifferential equations with unboundeddelay Our purpose in this

Ngày tải lên: 22/06/2014, 22:20

... subadjoint equation are established Keywords Linear singular difference equations· Differential algebraic equations · Adjoint equations· Subadjoint equations · Discrete Lagrange identity Mathematics ... For index-1 linear singular difference equations, the concept of the subadjoint equation is analysed in full detail based on the Kronecker normal form and the inherent regular ordinary difference ... Trang 1DOI 10.1007/s10013-013-0003-9Subadjoint Equations of Index-1 Linear Singular Difference Equations Le Cong Loi Received: 12 December 2011 / Published online: 30

Ngày tải lên: 15/12/2017, 04:40

... HOANG, Stability of a class of singular difference equations, Inter J Difference Equ., 1, 181-193 (2006) [2] P K Anh, N H Du, L C Loi, Singular difference equations: an overview, Vietnam J Math ... difference equations and differential-algebraic equations, Acta Math Vietnam 29 (2004), pp 23-39 [4] P K Anh, H T N Yen, On the solvability of initial-value problems for nonlinear implicit difference ... two above results for the constant coefficient implicit difference equations with perturbations in both sides Consider the linear implicit difference equation with constant coefficient Ex n + =

Ngày tải lên: 15/12/2017, 05:35