system of two second order linear differential equations
báo cáo hóa học:" Research Article Error Bounds for Asymptotic Solutions of Second-Order Linear Difference Equations II: The First Case" pot
... solutions of second- order linear difference equations II: the second case is dedicated to the case whenk<0.1.1. The Result in [3] When k 1When k 1, from 3 we know that 1.2 has two linearly ... completed the estimate of the error bounds for asymptotic solutions to second order linear difference equations in the first case. For the second case, we leave it to the second part of this paper: Error ... second- order linear difference equations, ” Journal of Computational and Applied Mathematics, vol. 41, no. 1-2, pp. 65–94, 1992.3 R. Wong and H. Li, “Asymptotic expansions for second- order linear...
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Báo cáo hoa học: " Research Article On Connection between Second-Order Delay Differential Equations and Integrodifferential Equations with Delay" pdf
... Difference Equations Volume 2010, Article ID 143298, 8 pagesdoi:10.1155/2010/143298Research ArticleOn Connection between Second- Order Delay Differential Equations and Integrodifferential Equations ... obtained by transforming second- order delay dierential equations ăxtat xgt btxht 0 to first -order differential equations. 1. Introduction and PreliminariesThe second order delay dierential equationăxt ... defined by 2.5.Proof. In the proof we will use notation defined in the proof of Theorem 2.1. The existenceand uniqueness of a solution of 1.11, 2.1 is a consequence of Theorem 2.1. Thus,...
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Báo cáo hóa học: " Research Article Sturm-Picone Comparison Theorem of Second-Order Linear Equations on Time Scales" ppt
... theorem of solution for second order nonlinear differential equations, ” Annals of Differential Equations, vol. 19, no. 3, pp. 480–486, 2003.7 R K. Zhuang and H W. Wu, “Sturm comparison theorem of ... theorem of second- order differential equations see Section 1.Remark 3.6. In the discrete case: μt ≡ 1. This result is the same as Sturm comparison theorem of second- order difference equations ... of second- order linear equations on timescales. We first establish Picone identity on time scales and obtain our main result by using it.Also, our result unifies the existing ones of second- order...
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báo cáo hóa học:" Research Article Limit Properties of Solutions of Singular Second-Order Differential Equations" doc
... ArticleLimit Properties of Solutions of Singular Second- Order Differential Equations Irena Rach˚unkov´a,1Svatoslav Stanek,1Ewa Weinmăuller,2and Michael Zenz21Department of Mathematical ... thesolvability of nonlinear singular equations subject to different types of boundary conditions.In this section, we utilize Theorem 4.1 to show the existence of solutions for periodicproblems. The rest of ... sufficient conditions for the existence of at leastone solution of problem 5.1a and 5.1b with a>0. In the proof of this theorem, we workalso with auxiliary two- point boundary conditions:u0...
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Báo cáo hóa học: " Research Article Global Behavior of Solutions to Two Classes of Second-Order Rational Difference Equations Sukanya Basu and Orlando Meri" docx
... ArticleGlobal Behavior of Solutions to Two Classes of Second- Order Rational Difference Equations Sukanya Basu and Orlando MerinoDepartment of Mathematics, University of Rhode Island, Kingston, ... Dynamics of Second Order Rational Difference Equations, Chapman &Hall/CRC, Boca Raton, Fla, USA, 2002.2 G. Ladas, “Invariants for generalized Lyness equations, ” Journal of Difference Equations ... about the global dynamics of 1.11 and 1.13, such asthe character of the prime period -two solutions to either equation, or even for more generalrational second- order equations, when such solutions...
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galois theory of linear differential equations - m. van der put, m. singer
... translates into ZL=(ra,b)GL. A proof of Lemma 1.29 finishesthe proof of the theorem. ✷Proof of lemma 1.29.The proof is rather similar to the one of lemma 1.23. The only thing that wehave ... as a group of matricesand has the structure of a linear algebraic group, that is, it is a group of invertiblematrices defined by the vanishing of a set of polynomials on the entries of thesematrices. ... O-submodules N1,N2 of N with N = N1⊕N2and Ni= Fifor i =1, 2.Proof. The proof is similar to the proof of Proposition 3.17. Let S1and S2be the set of eigenvalues of E acting on F1and...
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báo cáo hóa học:" Research Article Multiple Positive Solutions of a Singular Emden-Fowler Type Problem for Second-Order Impulsive Differential Systems" pdf
... Hu, and Y. Wu, “Positive solutions of two- point boundary value problems for systems of nonlinear second- order singular and impulsive differential equations, ” Nonlinear Analysis: Theory,Methods ... S. G. Hristova and D. D. Ba˘ınov, “Existence of periodic solutions of nonlinear systems of differential equations with impulse effect,” Journal of Mathematical Analysis and Applications, vol. ... 3-4, pp. 307–328, 2004.4 B. Liu and J. Yu, “Existence of solution of m-point boundary value problems of second- order differential systems with impulses,” Applied Mathematics and Computation,...
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Báo cáo sinh học: " Research Article Existence and Lyapunov Stability of Periodic Solutions for Generalized Higher-Order Neutral Differential Equations" potx
... Journal of Mathematical Analysis and Applications, vol. 326, no. 2, pp. 1161–1173,2007.9 J. Wu and Z. Wang, Two periodic solutions of second- order neutral functional differential equations, ” ... Journal of Mathematical Analysis and Applications, vol. 329, no. 1, pp. 677–689, 2007.10 M. R. Zhang, “Periodic solutions of linear and quasilinear neutral functional-differential equations, ”Journal ... and Lyapunov Stability of Periodic Solutions for Generalized Higher -Order Neutral Differential Equations Jingli Ren,1Wing-Sum Cheung,2and Zhibo Cheng11Department of Mathematics, Zhengzhou...
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Báo cáo sinh học: " Research Article Multiple Positive Solutions of Fourth-Order Impulsive Differential Equations with Integral Boundary Conditions and One-Dimensional p-Laplacian" ppt
... introduction of the basic theory of impulsivedifferential equations, see Lakshmikantham et al. 1; for an overview of existing results and of recent research areas of impulsive differential equations, ... Differential Equations, vol. 14, World Scientific,Singapore, 1995.6 J. Yan, “Existence of positive periodic solutions of impulsive functional differential equations with two parameters,” Journal of Mathematical ... olutionyt,t∈ J with property 3.17.Proof. The proof is similar to that of Theorem 3. 2of 6.Theorem 3.5. Assume that H1, H2, 3.1 of H3 and 3.14 and 3.15 of H4 hold. Inaddition,...
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Báo cáo sinh học: "Homoclinic solutions of some second-order non-periodic discrete systems" ppt
... is just the repetition of the proof of Lemma 3.2, we omit the details of its proof.With the aid of above preparations, now we will give the proof of Theorem1.2.Proof of Theorem 1.2 By(1.8), ... is in some way a type of the best expressive way of the structure of the solution space for recurrence relations occurring in the study of second- order linear differential equations. So, (1.3) ... similar to the proof of Lemma 3.1, sowe omit the details of its proof.Lemma 3.4 Under the conditions of Theorem 1.2, F (x) satisfies the PScondition.Proof From the proof of Lemma 3.2, we see...
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báo cáo hóa học:" Homoclinic solutions of some second-order non-periodic discrete systems" doc
... is just the repetition of the proof of Lemma 3.2, we omit the details of its proof.With the aid of above preparations, now we will give the proof of Theorem1.2.Proof of Theorem 1.2 By(1.8), ... similar to the proof of Lemma 3.1, sowe omit the details of its proof.Lemma 3.4 Under the conditions of Theorem 1.2, F (x) satisfies the PScondition.Proof From the proof of Lemma 3.2, we see ... is in some way a type of the best expressive way of the structure of the solution space for recurrence relations occurring in the study of second- order linear differential equations. So, (1.3)...
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