solving linear differential equations with constant coefficients

... Trang 1Stability Radius of Linear Dynamic Equations with Constant Coefficients on Time Scales Le Hong Lan!*, Nguyen Chi Liem? | Department of ... (1—a)A] < 0}, where we use the convention In0 = —oo 5 Stability radius of linear dynamic equations with constant coefficients on time scales Assume that the nominal equation is uniformly exponentially ... and formula of the stability radius were extended to linear time-invariant differential-algebraic systems [6, 7]; and to linear time-varying differential and difference-algebraic systems [8, 9]

Ngày tải lên: 22/03/2014, 11:20

... -o))l < 0), where we use the convention lnO : -oo. 5 Stability radius of linear dynamic equations with constant coefficients on time scales Assume that the nominal equation is uniformly exponentially ... and formula of the stability radius were extended to linear time-invariant differential-algebraic systems [6, 7]; and to linear time-varying differential and difference-algebraic systems [g, 9]. ... time-invarying dynamic equations with respect to linear dynamic pe(urbations on time scales A formula for the stability radius is given. Keywords and phrases : time scales, exponential function, linear dynamic

Ngày tải lên: 14/12/2017, 14:52

... motivation of our investigation goes back to [10] dealing with the linear system of differential equations with constant coeffi-cients and constant delay One of the systems considered has the form ... develop a method for construction of solutions of linear discrete systems with constant coefficients and with pure delay Solutions are expressed with the aid of a special function called the discrete ... notationZq s or another one with a couple of integerss, q, we suppose s ≤ q In this paper we deal with the discrete system wherem ≥1 is a fixed integer,k ∈ Z ∞ 0,B =(b i j) is a constantn × n matrix,

Ngày tải lên: 22/06/2014, 22:20

... Trang 1HIGHER-ORDER LINEAR DIFFERENTIAL EQUATIONSWITH STRONG SINGULARITIES R P AGARWAL AND I KIGURADZE Received 4 April 2004; Revised ... December 2004; Accepted 14 December 2004 For strongly singular higher-order linear differential equations together with two-pointconjugate and right-focal boundary conditions, we provide easily ... b[) (L2α,β(]a, b[)) is the space of integrable (square integrable) with the weight (t − a) α(b − t) βfunctionsy :]a, b[ → Rwith the norm α(]a, b])) is the space of functions y ∈ Lloc(]a, b[)

Ngày tải lên: 23/06/2014, 00:20

... C2 holds for κ 1 = κ 2 = 1 +ε, L 1 ∈ R, L 2 ≥ 0 with a constant ε > 0 This, combined with Condition C4 and Cauchy’s inequality, implies that, with Le= max{3, L 1 , L 2 } for any x, x∈R d and ... evy-driven McKean-Vlasov SDEs with irregular coefficientsIn this section, we present results concerning the exact solution of the McKean-Vlasov stochastic differential equation with jumps (3.1) First, ... u(t)≤c+Z t 0 v(s)u(s)ds for all 0≤t≤T, then u(t)≤cexpStochastic differential equationsLet (Ω,F, P) be a complete probability space with a filtration {F t } t≥0 satisfying the usual conditions LetWt

Ngày tải lên: 17/09/2025, 16:23

... Article On the Spectrum of Almost Periodic Solution of Second-Order Neutral Delay Differential Equations with Piecewise Constant of Argument Li Wang and Chuanyi Zhang Department of Mathematics, Harbin ... Differential equations with piecewise constant argument, which were firstly considered by Cooke and Wiener1 and Shah and Wiener 2, combine properties of both differential and difference equations ... spectrum containment of almost periodic solution of second-order neutral delay differential equations with piecewise constant of argumentEPCA, for short of the form xt  pxt − 1 qx 2t 

Ngày tải lên: 21/06/2014, 20:20

... existence of periodic solutions to differential equation with piecewise constant argument In this note, we are concernded with differential equations with piecewise constant argument of the form ... ordinary differential equations, saying that the linear differential equation of the form b= Alt)e(t) + f(t), where A, f is continuous, periodic with the same period 7, has a periodic solution with ... C", (1.1) where A is a linear operator on C”, f is a bounded continuous function from R to C”, |.| is the largest integer function Differential equations with piecewise constant argument have

Ngày tải lên: 11/03/2015, 07:57

... solutions to differential equation with piecewise constant argument 2003 Published by Elsevier Inc 1 Introduction In this paper, we are concerned with differential equations with piecewise constant ... the form where A is a linear operator on C n , f is a bounded continuous function from R to C n,[·] is the largest integer function Differential equations with piecewise constant argument have ... Trang 1Massera criterion for periodic solutionsof differential equations with piecewise constant argument N.T Thanh Department of Mathematics, Hanoi University of Science,

Ngày tải lên: 16/12/2017, 16:50

... solutions.First-order differential equations with state-dependent deviated argu-ments have received a lot of attention in the last years We can cite therecent articles [2–7] which deal with existence ... original work is properly cited. Trang 2Minimal and maximal solutions to first-order differential equations with state-dependent deviated argumentsRub´en Figueroa∗ and Rodrigo L´opez Pouso Department ... concerned with the existence of solutions for the following problem with deviated arguments: where f : I × R2−→ R and τ : I0× C(I) −→ I are Carath´eodory functions, Λ : C(I) −→ R is a continuous nonlinear

Ngày tải lên: 20/06/2014, 20:20

... neutral nonlinear differential equations with delay. Nonlinear Anal 74(12):3926 –3933 (2011) doi:10.1016/j.na.2011.02.029 17 Raffoul, YN: Stability in neutral nonlinear differential equations with ... with Sakthivel and Luo [11,12] investigate the asymptotic stability of the non-linear impulsive stochastic differential equations and the impulsive stochastic partial differential equations with ... neutral differential equations with variable delays Proc Am Math Soc 136, 909 –918 (2008) 19 Ardjouni, A, Djoudi, A: Fixed points and stability in linear neutral differential equations with variable

Ngày tải lên: 20/06/2014, 22:20

... 325415, 16 pagesdoi:10.1155/2010/325415 Research Article Variational Approach to Impulsive Differential Equations with Dirichlet Boundary Conditions Huiwen Chen and Jianli Li Department of Mathematics, ... study the existence of n distinct pairs of nontrivial solutions for impulsive differential equations with Dirichlet boundary conditions by using variational methods and critical point theory 1 ... impulsive differential equations In recent years, many researchers have used some fixed point theorems6,7, topological degree theory 8, and the method of lower and upper solutions with monotone iterative

Ngày tải lên: 21/06/2014, 11:20

... pagesdoi:10.1155/2011/654871 Research Article Multiple Positive Solutions of Fourth-Order Impulsive Differential Equations with Integral Boundary Conditions and One-Dimensional p-Laplacian Meiqiang Feng School ... of integral equations and their relation with boundary-value problems, we refer to the book of Corduneanu22 and Agarwal and O’Regan 23.On the other hand, boundary-value problems with integral ... theory of impulsivedifferential equations, see Lakshmikantham et al 1; for an overview of existing results and of recent research areas of impulsive differential equations, see Benchohra et al

Ngày tải lên: 21/06/2014, 16:20

... made available soon Extremal solutions for certain type of fractional differential equations with maxima Advances in Difference Equations 2012, 2012:7 doi:10.1186/1687-1847-2012-7 Rabha W Ibrahim ... differential equations, because some boundary conditions are automatically fulfilled and due to lower order differ-ential requirements (see [9]) Differential equations with maximum arise naturally when solving ... http://www.springeropen.com Advances in Difference Equations © 2012 Ibrahim ; licensee Springer. Trang 2Extremal solutions for certain type of fractional differential equations with maxima Rabha W Ibrahim Institute

Ngày tải lên: 21/06/2014, 17:20

... Nonlocal nonlinear differential equations with a measure of noncompactness in Banach spaces Nonlinear Anal TMA 70, 2593–2601 (2009) [15] Xue, XM: L p theory for semilinear nonlocal problems with measure ... governed by semilinear differentialinclusions in a Banach space with a noncompact semigroup Nonlinear Anal TMA 70,3424–3436 (2009) [13] Xue, XM: Semilinear nonlocal problems without the assumptions ... AbstractThis article is concerned with impulsive semilinear differential equations with nonlocalinitial conditions in Banach spaces The approach used is fixed point theorem combinedwith the technique of

Ngày tải lên: 21/06/2014, 17:20

... deal with the stability for deterministic differential equations, not for stochastic differential equations Very recently, Luo 6 studied the mean square asymptotic stability for a class of linear ... stability of a generalized linear neutral stochastic differential equation with variable delays by using the fixed point theory An asymptotic mean square stability theorem with a necessary and sufficient ... pagesdoi:10.1155/2008/407352 Research Article Fixed Points and Stability in Neutral Stochastic Differential Equations with Variable Delays Meng Wu, 1 Nan-jing Huang, 1 and Chang-Wen Zhao 2 1 Department

Ngày tải lên: 21/06/2014, 23:20

... pagesdoi:10.1155/2007/52304 Research Article On the Kneser-Type Solutions for Two-Dimensional Linear Differential Systems with Deviating Arguments Alexander Domoshnitsky and Roman Koplatadze Received 7 January ... the con-ditionu1(t)u2(t) < 0 for t∈[t0, +∞) Note one of our results obtained for this systemwith constant coefficients and delays (p(t)≡ p,q(t) ≡ q,τ(t) = t − Δ,σ(t) = t − δ, where δ,Δ ∈ RandΔ ... original work is prop-erly cited dis-1 Introduction The equationu (t)= pu(t), t ∈[0, +∞) with positive constant coefficient p, has two lin-early independent solutionsu1= e √ ptandu2= e −√ pt The

Ngày tải lên: 22/06/2014, 18:20

... pagesdoi:10.1155/2007/98423 Research Article Oscillation of Higher-Order Neutral-Type Periodic Differential Equations with Distributed Arguments R S Dahiya and A Zafer Received 19 October 2006; Accepted ... numbers with λ > 0 and μ > 0. Trang 3We may begin with the following comparison theorem.Theorem 2.1 Let δ = 1, α ≥ 0, β < 0, and 1 + α + β > 0 Suppose that (a) equation ( E k μ ) with ... solution of degree n; (b) equation ( E λ h ) with λ = − β and h = − τ has no eventually positive solution of degree 0 whenever n is odd; (c) equation ( E μ k ) with μ =1 +α and k = τ has no eventually

Ngày tải lên: 22/06/2014, 18:20

... superlinear growth of the nonlinearity of f (t, p) in p  Inspired by [21,24,25], in this paper, we investigate the following second-order impul-sive nonlinear differential equations with periodic ... pagesdoi:10.1155/2007/41589 Research Article Existence of Solutions for Second-Order Nonlinear Impulsive Differential Equations with Periodic Boundary Value Conditions Chuanzhi Bai and Dandan Yang Received ... of impulsive differential equations to different areas, for example, see [6–15] Boundary value problems (BVPs) for impulsive differential equations and im-pulsive difference equations [16–20] have

Ngày tải lên: 22/06/2014, 19:20

... pagesdoi:10.1155/2007/49125 Research Article Semigroup Approach to Semilinear Partial Functional Differential Equations with Infinite Delay Hassane Bouzahir Received 6 November 2006; Revised ... describe a semigroup of abstract semilinear functional differential equations with infinite delay by the use of the Crandall Liggett theorem We suppose that the linear part is not necessarily densely ... (semi)normed abstract linear space of functions mapping (−∞, 0] intoE, which satisfies the following. (A) There is a positive constantH and functions K( ·),M( ·) :R +→ R+, withK con-tinuous andM

Ngày tải lên: 22/06/2014, 22:20

... 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 equation with ... k , 0≤ k ≤ N − n − m, can be computed without any knowledge of the boundary conditionsy N − k = β k, 0≤ k ≤ m −1 By analogy with the case of differential equations, we can say that there arem ... compared with the singular perturbation method We consider a right end perturbation (small parameters are situated on the right), and we deduce the results from Section 2 The comparison with the

Ngày tải lên: 22/06/2014, 22:20