solving second order systems of differential equations

... 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 Institute of ... Dosly The spectrum containment of almost periodic solution of second- order neutral delay differential equations with piecewise constant of argument EPCA, for short of the form xtpxt − 1   qx2t ... contradiction. The claim follows. 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...

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... BVPs of singular differential equations, ” Proceedings of the Royal Society of Edinburgh. Section A, vol. 128, no. 5, pp. 1099–1114, 1998. 10 M. Zhang, “Periodic solutions of damped differential systems ... Torres, “Existence and stability of periodic solutions for second- order semilinear differential equations with a singular nonlinearity,” Proceedings of the Royal Society of Edinburgh. Section A, vol. 137, ... “Existence of one-signed periodic solutions of some second- order differential equations via a Krasnoselskii fixed point theorem,” Journal of Differential Equations, vol. 190, no. 2, pp. 643–662, 2003. 38...

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... Difference Equations 2011, 2011:14 http://www.advancesindifferenceequations.com/content/2011/1/14 Page 14 of 17 RESEARCH Open Access Some new results for BVPs of first -order nonlinear integro -differential ... the existence of solutions for first -order nonlinear integro -differential equations with boundary value conditions. Our methods to prove the existence of solutions involve new differential inequalities and ... first order impulsive integro -differential equations of mixed type. J Math Anal Appl. 296,8–20 (2004). doi:10.1016/j.jmaa.2003.12.047 8. Jankowski, T, Jankowski, R: On integro -differential equations...

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... asymptotic properties of solutions of even order neutral difference equations. J. Diff. Equ. Appl. 15 , 1077–1084 (2009) [5] Agarwal, RP, Grace, SR: The oscillation of certain difference equations. Math. ... Grace, SR: Oscillation of certain difference equations of mixed type. J. Math. Anal. Appl. 224, 241–254 (1998) [7] Gyori, I, Laddas, G: Oscillation Theory of Delay Differential Equations. Clarendon ... will be made available soon. Oscillation criteria for second- order nonlinear neutral difference equations of mixed type Advances in Difference Equations 2012, 2012:4 doi:10.1186/1687-1847-2012-4 Ethiraju...

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... 2009. 10 Advances in Difference Equations 22 T. Li, Z. Han, and S. Sun, “Oscillation of one kind of second- order delay dynamic equations on time scales,” Journal of Jishou University, vol. 30, ... for second- order delay dynamic equations on time scales,” Advances in Difference Equations, vol. 2007, Article ID 70730, 16 pages, 2007.  14 Z. Han, B. Shi, and S R. Sun, “Oscillation of second- order ... Journal of University of Jinan, vol. 23, no. 3, pp. 299–301, 2009. 20 T. Li and Z. Han, “Oscillation of certain second- order neutral difference equation with oscillating coefficient,” Journal of University...

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... equal to I. The proof of uniqueness is complete. To prove the existence we note, first of all, that it suffices to provide a proof if one of the κ i ’s is equal to ±1 and one of the δ j ’s is equal ... for all k ∈ Z. The proof of the first part of Theorem 4.9 is complete. In order to prove Theorem 4.9(ii), we need to compare the first and the third factors of the two sides of (4.7). The first factors ... solutions of isomonodromy problems for such systems of difference equations. In the case of one-interval gap probability this has been done (in a different language) in [Bor], [BB]. One example of the...

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... properties of the channel capacity C(t). Again, by applying the concept of transformation of random variables, the PDF p C (r) of the channel capacity 8 On the first- and second- order statistics of the capacity ... process. The second- order statistical properties of multihop Rayleigh fading channels have been studied in [15], while for dualhop Nakagami-m channels, the second- order statistics of the received ... LCR N C (r) of the capacity C(t) of N∗Nakagami-m channels. It can be observed that at lower levels r , the LCR N C (r) of the capacity of N∗Nakagami-m channels with lower values of the fading...

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... polynomial solutions of a class of linear differential equations of the second order. Bull A M S. 36, 77–84 (1930). doi:10.1090/S0002-9904-1930-04888-0 Azad et al. Advances in Difference Equations 2011, ... which is an eigenfunction of L. Specializing to second- order equations because of their importance in applications– and leaving in this article the higher -order case because of its technical complexity–the canonical ... Advances in Difference Equations 2011, 2011:58 http://www.advancesindifferenceequations.com/content/2011/1/58 Page 6 of 12 3 Canonical forms of self-adjoint second- order equations with polynomial coefficients Let...

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... 2011:151 http://jwcn.eurasipjournals.com/content/2011/1/151 Page 6 of 7 about the second- order st atist ics of var ious diversity sys- tems can be easily found in the literature [13-15]. Second- order statistics analysis of macro-diversity ... the order of Gamma distribution, the measure of the shadowing pre- sent in the channels. Ω 01 and Ω 02 are related to the aver- age powers of the Gamma long-term fading distributions. 3 Second- order ... Karagiannidis, On the second order statistics of the multihop Rayleigh fading channel. IEEE Trans Commun. 57(6), 1815–1823 (2009) 16. D Stefanovic, SR Panic, P Spalevic, Second- order statistics of SC macrodiversity...

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... second example, we will obtain the bound of the solutions of an integral equation. For the sake of proving the global existence of solutions of differential equations, we first recall some basic ... in order to illustrate the validity of the above results. In the first example, we will try to prove the global existence of the solu- tions of a delay differential equation, while in the second ... integral equation, differential equa- tion, bounded 1 Introduction During the past decades, with the development of the theory of differential and integral equations, a lot of integral inequalities,...

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... forced second- order mixed type quasilinear delay differential equations, ” Electronic Journal of Differential Equations, p. No. 73, 9, 2010. 13 Y. G. Sun and F. W. Meng, “Oscillation of second- order ... for second- order forced dynamic equations with mixed nonlinearities,” Advances in Difference Equations, vol. 2009, Article ID 938706, 20 pages, 2009. 11 C. Li and S. Chen, “Oscillation of second- order ... Difference Equations 8 J. Shao and F. Meng, “Oscillation theorems for second- order forced neutral nonlinear differential equations with delayed argument,” International Journal of Differential Equations, ...

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... properties of the third -order differential equations see 1–20. Various techniques appeared for the investigation of such equations. Some of them 1, 19 make use of the methods developed for the second- order ... properties of E with the help of E C . Without loss of generality, we can deal only with the positive solutions of E. Since every solution of E is also a solution of E C , we are in view of ... behavior of the above-mentioned equation from the oscillation of a couple of the first -order differential equations. Obtained comparison principles essentially simplify the examination of the studied equations. 1....

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