... perturbation method applied to the open-loop discrete optimalcontrol problem, Optimal Control Applications & Methods 3 (1982), no. 2, 121–131.[15] T. Sari and T. Zerizer, Perturbations for linear ... convergence of theproposed iterative method. Section 3 is mainly devoted to validate the effectiveness ofour method, compared with the singular perturbation method. We consider a right endperturbation ... comparison with the other formal method requires the analysis of its re-sults. We conclude with Section 4.2. Main result2.1. Formal asymptotic solution. In this section, we develop a perturbation method...
... VietnamReceived 10 August 2010Abstract. This paper deals with a formula of stability radii for an lineardifference equation(LDEs for short) with the coefficients varying in time under structured ... operator. The result is considered as an discrete version ofa previous result for time-varying ordinary differential equations [1].Keywords: Robust stability, Lineardifference equation, Input-output ... Kd.VNU Journal of Science, Mathematics - Physics 26 (2010) 175-184Stability Radii for DifferenceEquationswith Time-varyingCoefficientsLe Hong Lan*Department of Basic Sciences, University...
... becomes differenceequationswith distrib-uted delays without impulses in vector formx(m +1)=Ax(m)+Bf (x(m)) + C∞k=1μkg (x(m − k)),(24)which contains many popular models such as discrete- time ... with aftereffect. In: Translations of Mathematical Monographs, vol.157,American Mathematical Society, Providence, RI (1996)2. Xu, DY: Asymptotic behavior of nonlinear differenceequationswith ... ConclusionIn this paper, we consider a class of impulsive differenceequationswith distributeddelays. By establishing an impulsive delay difference inequality and using the propertiesof “r-cone”...
... nonlinear first-order difference equation.2 Advances in Difference Equations Unlike t he method used by Olver 4 to treat asymptotic solutions of second-order linear differential equations, the method ... in Difference Equations Volume 2010, Article ID 594783, 19 pagesdoi:10.1155/2010/594783Research ArticleError Bounds for Asymptotic Solutions ofSecond-Order LinearDifferenceEquations II:The ... of αi,ρiin 1.5, 1.7,and2p − q 1.Equation 3.8 is a second-order linear difference equation with two known linear independent solutions. Its coefficients are quite similar to those in...
... Regularly Varying Solutions of H alf -Linear Difference Equations In this short section we show how the results of Section 3 can be extended to half -linear difference equations of the formΔΦΔyk ... asecond-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 ... order linear difference equations, ”Fasciculi Mathematici, no. 31, pp. 71–89, 2001.9 M. Cecchi, Z. Doˇsl´a, and M. Marini, “Positive decreasing solutions of quasi -linear difference equations, ”...
... 1.2 with α 0, and λj−K0 ≤ j ≤ N −1 denotes the eigenvalue of the problem 1.1 and 1.2 with α π. We now present the main results of this paper.Advances in Difference Equations 13linearly ... CorporationAdvances in Difference Equations Volume 2009, Article ID 347291, 18 pagesdoi:10.1155/2009/347291Research ArticleInequalities among Eigenvalues ofSecond-Order DifferenceEquations with General Coupled ... 1.2 with α 0 or α π.If fλ2 or −2 for some λ/ μk0 ≤ k ≤ Ns,thenλ is a simple eigenvalue of 1.1 and 1.2 with α 0 or α π and for every λ/ μk0 ≤ k ≤ Ns ,with 2...
... difference equationswithdiscrete variable have attracted considerableattention. In particular, delay effect on the asymptotic behavior and other behaviors ofimpulsive difference equationswithdiscrete ... of difference equations, specially, of difference equationswith continuousvariables. In the recent years, the asymptotic behavior and other behavior of delay difference equations with continuous ... impulsive delay difference equationswith continuousvariables,” Computers & Mathematics with Applications, vol. 55, no. 12, pp. 2732–2739, 2008.Advances in Difference Equations 3where xtx1t,...
... Difference Equations 18 O. Doˇsl´y and S. Fiˇsnarov´a, “Linearized Riccati technique and non-oscillation criteria for half -linear difference equations, ” Advances in Difference Equations, ... half -linear difference equations, ” Journal of Difference Equations and Applications, vol. 7, no. 4, pp. 483–505, 2001.5 P.ˇReh´ak, “Oscillation and nonoscillation criteria for second order linear ... half -linear second order difference equations, ” Journalof Difference Equations and Applications, vol. 9, no. 1, pp. 49–61, 2003.8 M. Cecchi, Z. Doˇsl´a, and M. Marini, “Nonoscillatory half-linear...
... CorporationAdvances in Difference Equations Volume 2008, Article ID 718408, 21 pagesdoi:10.1155/2008/718408Research ArticleStability of Equilibrium Points of Fractional Difference Equationswith Stochastic ... stochastic linear difference equations, ” Applied Mathematics Letters, vol. 10, no. 3, pp. 111–115, 1997.47 B. Paternoster and L. Shaikhet, “About stability of nonlinear stochastic difference equations, ” ... equivalent to the stability of theequilibrium point of 2.1.Together with nonlinear equation 2.2 we will consider and its linear partzn1kj0γjzn−j σznξn1,γjaj− bjxλ...
... andrelevant nonlinear equations has been an intensively developed area during the last twodecades.Let us compare stability methods for delay differential equations and delay difference equations. ... Many of the methods previously used for differential equations have also beenapplied to difference equations. However, there are at least two methods which are specificfor difference equations. ... ofdifference equations, ” Functional Differential Equations , vol. 15, no. 3-4, pp. 239–248, 2008.13 H. Matsunaga, T. Hara, and S. Sakata, “Global attractivity for a nonlinear difference equation with variable...
... ON kTH-ORDER LINEAR FUNCTIONAL EQUATIONS WITH CONSTANT COEFFICIENTSJITKA LAITOCHOV´AReceived 30 January 2006; Accepted 18 May 2006Abel functional equations are associated to a linear homogeneous ... functional equation, and linear homogeneous functional equa-tion in S with constant coefficients. T he classical theory of linear homogeneous functionaland difference equations is obtained as ... solution of the formf= λα(x), (3.3)where α satisfies Abel equation (3.1). Linear system (3.2)isalineardifference equation with constant coefficients of theformakf (x + k)+ak−1f (x + k − 1) +...