second order linear differential equation ppt

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... the solutions being oscillating for a class of linear second- order delayed-discrete equations. We consider the delayed second- order linear discrete equation Δx  n   −p  n  x  n − 1  , 1.1 where ... original work is properly cited. A linear second- order discrete-delayed equation Δxn−pnxn − 1 with a positive coefficient p is considered for n →∞. This equation is known to have a positive ... Corporation Advances in Difference Equations Volume 2010, Article ID 693867, 12 pages doi:10.1155/2010/693867 Research Article Oscillation of Solutions of a Linear Second- Order Discrete-Delayed Equation J. Ba ˇ stinec, 1 J....

Ngày tải lên: 21/06/2014, 18:20

... 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 solution for second ... theorem of second- order differential equations see Section 1. Remark 3.6. In the discrete case: μt ≡ 1. This result is the same as Sturm comparison theorem of second- order difference equations ... of second- order linear equations on time scales. 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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... for second order self-adjoint difference equation. J Math Anal Appl. 323, 513–521 (2006). doi:10.1016/j.jmaa.2005.10.049 18. Ma, MJ, Guo, ZM: Homoclinic orbits and subharmonics for nonlinear second ... Functional Differencial Equations. Kluwer Academic Publishers, Dordrecht (2000) 4. Guo, ZM, Yu, JS: The existence of subharmonic solutions for superlinear second order difference equations. Sci China. 33, ... homoclinic solutions for the following second- order non-autonomous discrete system Long Advances in Difference Equations 2011, 2011:64 http://www.advancesindifferenceequations.com/content/2011/1/64 â...

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... Difference Equations 2011, 2011:56 http://www.advancesindifferenceequations.com/content/2011/1/56 Page 8 of 8 RESEARC H Open Access Positive periodic solution of higher -order functional difference equation Mei-Lan ... models are first -order functional difference equations. Rela- tively, few articles focused on the existence of positive periodic solutions of higher -order functional difference equations. In 2010, ... difference equations. Appl Math Comput. 161, 441–462 (2005). doi:10.1016/j.amc.2003.12.097 9. Wang, W, Chen, X: Positive periodic solutions for higher order functional difference equation. Appl...

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... RESEARCH Open Access On a class of second- order nonlinear difference equation Li Dongsheng 1* , Zou Shuliang 1 and Liao Maoxin 2 * Correspondence: lds1010@sina. com 1 School ... kind of second- order rational difference equation. With the change of the initial values, we find the successive lengths of positive and negative semicycles for oscillatory solutions of this equation, ... stability Theorem 3.5. The positive equilibrium point of Equation (1.1) is locally asymptotically stable. Proof. The linearized equation of Equation (1.1) about the positive equilibrium point ¯ x is y n+1 =0· y n +0· y n−1 ,...

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... 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 Bound for Asymptotic Solutions of Second- order Linear ... “summary equation 2.1. Next we consider a 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 ... 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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... solutions of two-point boundary value problems for systems of nonlinear second- order singular and impulsive differential equations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 69, ... Grant. References 1 S. C. Hu and V. Lakshmikantham, “Periodic boundary value problems for second order impulsive differential systems,” Nonlinear Analysis: Theory, Methods & Applications, vol. 13, no. 1, pp. ... pages doi:10.1155/2011/212980 Research Article Multiple Positive Solutions of a Singular Emden-Fowler Type Problem for Second- Order Impulsive Differential Systems Eun Kyoung Lee and Yong-Hoon Lee Department of Mathematics, Pusan...

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... distribution and trace formula of a second order operator- differential equation Nigar Mahar Aslanova 1,2 Correspondence: nigar. aslanova@yahoo.com 1 Department of Differential Equation, Institute of Mathematics and ... problems for differential- operator equations. Nauk Dumka, Kiev, 284 (1984) (Russian). 31. Yakubov, S, Yakubov, Ya: Differential- Operator Equations Ordinary and Partial Differential Equations. Chapman ... simple identity for eigenvalue of second order differential operator. DAN SSSR. 88(4), 593–596 (1953) 19. Aslanova, NM: Trace formula for Sturm-Liouville operator equation. Proc Math Mech Natl Acad...

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... Difference Equations Volume 2009, Article ID 143175, 14 pages doi:10.1155/2009/143175 Research Article On the Spectrum of Almost Periodic Solution of Second- Order Neutral Delay Differential Equations with ... 14 Advances in Difference Equations 12 R. Yuan, “On the spectrum of almost periodic solution of second- order differential equations with piecewise constant argument,” Nonlinear Analysis: Theory, ... periodic differential equations and almost periodic flows,” Journal of Differential Equations, vol. 5, no. 1, pp. 167–181, 1969. 18 R. Yuan, “Pseudo-almost periodic solutions of second- order neutral...

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... for second order self-adjoint differ- ence equation. J. Math. Anal. Appl. 323, 513–521 (2006) [18] Ma, MJ, Guo, ZM: Homoclinic orbits and subharmonics for nonlinear second order difference equation. ... Functional Differencial Equations. Kluwer Academic Publishers, Dor- drecht (2000) [4] Guo, ZM, Yu, JS: The existence of subharmonic solutions for superlinear second order difference equations. Sci. China ... structure of the solution space for recurrence relations occurring in the study of second- order linear differential equations. So, (1.3) arises with high frequency in various fields such as optimal...

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