ONE PARAMETER FAMILY OF LINEAR DIFFERENCE EQUATIONS AND THE STABILITY PROBLEM FOR THE NUMERICAL pdf

... 5.2. The problem of stability for boundary value methodsAs mentioned in the Introduction, the study of the stability for dissipative nonlinearproblems is made by linearizing the nonlinearity ... around the asymptotically stable criticalpoint. This is equivalent to examine the behavior of the solutions of a numerical method ONE PARAMETER FAMILY OF LINEAR DIFFERENCE EQUATIONS AND THE STABILITY ... on the same parameter q. The order of the equation of the error is, usually, greater than the one of the diﬀerentialequation. Therefore, an higher number of conditions are needed to get the...

báo cáo hóa học:" Research Article Asymptotic Behavior of Equilibrium Point for a Family of Rational Difference Equations" docx

... IntroductionDiﬀerence equations appear naturally as discrete analogues and in the numerical solutions of diﬀerential and delay diﬀerential equations, and they have applications in biology, ecology,physics, and ... ecology,physics, and so forth 1. The study of properties of nonlinear diﬀerence equations has beenan area of intense interest in recent years. There has been a lot of work concerning the globally asymptotic ... condition for the local stability of the diﬀerence equationxnk s1xnk−1 ··· skxn 0,n 0, 1, 2.43. The Main Results and Their ProofsIn this section, we investigate the globally...

GLOBAL ATTRACTOR OF COUPLED DIFFERENCE EQUATIONS AND APPLICATIONS TO LOTKA-VOLTERRA SYSTEMS C. V. doc

... for the global attraction of (u∗,v∗)relativetothewhole space R2(or the positive cone R2+) for any of the three types of quasimonotonefunctions.Theorem 4.5. Let the conditions in Theorems ... initialfunctions for each of the above three types of quasimonotone functions. The comparisonresults for the ﬁrst two types of quasimonotone functions are based on the followingpositivity lemma for a ... of nonlinear diﬀerence equations which isa discrete approximation of a class of nonlinear diﬀerential systems with time delays. The aim of the paper is to show the existence and uniqueness of...

NONOSCILLATORY HALF-LINEAR DIFFERENCE EQUATIONS AND RECESSIVE SOLUTIONS ˇ ´ MARIELLA CECCHI, pdf

... (1.9)is, for large n, a solution of the generalized Riccati equation (1.6)andsoproperty(1.7)coincides with (1.5), stated in the linear case.In [11], the open problems whether analogous results as the ... \{0},∆unun<∆xnxn for large n. (3.1) The following theorem holds.198 Recessive solutions for half -linear equations Theorem 3.2 (see [11]). If (1.1) is nonoscillatory, recessive solutions of (1.1) exist and theyare ... 2.3 and we obtain un≡ 0forn ≥ N.This implies that x[1]n= z[1]n for every n ≥ N and the assertion easily follows. In view of the homogeneity property, from Theorem 3.4 we obtain the...

báo cáo hóa học:" Research Article Error Bounds for Asymptotic Solutions of Second-Order Linear Difference Equations II: The First Case" pot

... completed the estimate of the error bounds for asymptotic solutions to secondorder linear diﬀerence equations in the ﬁrst case. For the second case, we leave it to the secondpart of this paper: ... still open. The purpose of this and the next paper Errorbounds for asymptotic solutions of second-order linear diﬀerence equations II: the secondcase is to estimate error bounds for solutions ... k>0, and in the second case as k<0 where k  2p − q. The whole proof of the result is too long tounderstand, so we divide the estimations into two parts, part I this paper and part II the next...

Báo cáo hoa học: " Research Article Summation Characterization of the Recessive Solution for Half-Linear Difference Equations" doc

... 4.9then h is not the recessive solution.Proof. Similarly, as in the proof of Theorem 4.1, denote wk rkΦΔhk/hk and let wkbe asolution of 2.1 generated by another solution linearly ... Diﬀerential Equations, vol. 202 of North-Holland Mathematics Studies,Elsevier, Amsterdam, The Netherlands, 2005.17 M. Cecchi, Z. Doˇsl´a, and M. Marini, “On recessive and dominant solutions for ... 2.AcknowledgmentsThis research is supported by the Grant 201/07/0145 of the Czech Grant Agency of the CzechRepublic, and the Research Project MSM0022162409 of the Czech Ministry of Education.References1 P.ˇReh´ak,...

Báo cáo hóa học: "Research Article Periodic and Almost Periodic Solutions of Functional Difference Equations with Finite Delay" pdf

... that{u(n)}n≥0is ᐁᏭ᏿. Then the solution {uk(n)} of (4.4)isalsoᐁᏭ᏿ with the same pair (δ0,ε,N(ε)) as the one for {u(n)}n≥0.Let(δ∗(ε),ε) be the pair for uniform stability of {η(n)}. For any given ... Functions and Ergodicity, Science Press, Beijing, China; KluwerAcademic, Dordrecht, The Netherlands, 2003.[19] T. Yoshizawa, Stability Theory and the Existence of Periodic Solutions and Almost ... position to prove the following result.Theorem 4.4. Suppose that for each G∈ H(F), the solution of (4.2)isuniquefortheinitialcondition. If the bounded solution{u(n)}n≥0 of (4.1)isᐁᏭ᏿, then {u(n)}n≥0is...

Báo cáo hóa học: "Research Article Linearized Riccati Technique and (Non-)Oscillation Criteria for Half-Linear Difference Equations" docx

... by the Taylor formula for the functionFk,v :Rk vHk, v at the center v  0 see the com-putations in the proof of Theorem 4.1 and observe that 4.29 is still suﬃcient for the uniformconvergence ... distinguishbetween the cases p ≥ 2andp ∈ 1, 2. The last section of the paper is devoted to an application of the results of the previous sections of the paper.2. PreliminariesOscillatory properties of 1.1 ... essentially the same line as that of the previous theo-rem, with the only diﬀerence that Theorem 4.1 instead of Theorem 4.2 is used and, of course,2.7 is used instead of 2.8. However, Theorem...

PERIODIC SOLUTIONS FOR A COUPLED PAIR OF DELAY DIFFERENCE EQUATIONS GUANG ZHANG, SHUGUI KANG, AND potx

... ρ(K2) < 1.Then(1.3) has at least one pe riodic solution.Proof. Note that Ω0× Ω0is a normal solid cone of X × X.LetA1, A2,andA be the sameoperators in the proof of Theorem 2.1.Setgn=n+ω−1s=nG(n,s)hsbs, ... that (A2(u,v))ˇn σ(A2(u,v))n for any n,ˇn ∈ Z.Thus,A : Ω × Ω →Ω × Ω. Furthermore, in view of the boundedness of G and G, and the continuity of f1 and f2, it is not diﬃcult to show ... represent the size of a populationin the time per iod n. Since it is possible that the population may be inﬂuenced by an-other factor of the form−hnf2(n,xn−τ(n)), we are therefore interested...

ON THIRD-ORDER LINEAR DIFFERENCE EQUATIONS INVOLVING QUASI-DIFFERENCES ˇ ´ ˇ ZUZANA DOSLA AND pdf

... and the proof of Theorem 4.4,we get the fact that C is an oscillatory solution of (4.8). The opposite statement followsfrom Theorem 4.6.Open problems.(1) It is an open problem whether the ... 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 of oscillatory solutions ... (3.3) for each k∈ N such that 1 ≤ k<m. The proof follows from the proof of [3, Proposition 2]. The existence of Kneser solutions of (E) is ensured by the following result.Theorem 3.3. There...

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