system of first order differential equations examples

... solutions), unfortunately often identified in the literature on lower and upper solutions. First- order differential equations with state-dependent deviated argu- ments have received a lot of attention in ... compact set of fixed points in C(I), which are exactly the solutions of problem (4). Claim 2: Every solution x of (4) satisfies α ≤ x ≤ β on I and, therefore, it is a solution of (1) in [α, β]. First, ... [2–7] which deal with existence results for this kind of prob- lems. For the qualitative study of this type of problems we can cite the survey of Hartung et al. [8] and references therein. As main...

Ngày tải lên: 20/06/2014, 20:20

... a class of even -order differential equations Journal of Inequalities and Applications 2012, 2012:5 doi:10.1186/1029-242X-2012-5 Qi-Ming Zhang (zhqm20082008@sina.com) Xiaofei He (hexiaofei525@sina.com) ISSN ... for a class of even -order differential equations Qi-Ming Zhang ∗1 and Xiaofei He 2 1 College of Science, Hunan University of Technology, Zhuzhou, Hunan 412000, P.R. China 2 College of Mathematics ... of Lyapunov. Am. J. Math. 73, 885–890 (1951) [3] Cheng, SS: Lyapunov inequalities for differential and difference equations. Fasc. Math. 23, 25–41 (1991) [4] He, Z: Existence of two solutions of...

Ngày tải lên: 20/06/2014, 21:20

... delay dynamic equations of first order, ” Advances in Difference Equations, vol. 2008, Article ID 458687, 12 pages, 2008. 10 H. A. Agwo, “On the oscillation of first order delay dynamic equations with ... uniqueness of solutions to systems of delay dynamic equations on time scales,” http://arxiv.org/abs/1001.0737v3 . 6 M. Bohner, “Some oscillation criteria for first order delay dynamic equations, ” ... Article Nonoscillation of First- Order Dynamic Equations with Several Delays Elena Braverman 1 and Bas¸ak Karpuz 2 1 Department of Mathematics and Statistics, University of Calgary, 2500 University...

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Ngày tải lên: 23/06/2014, 00:20

... 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 ... for 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...

Ngày tải lên: 21/06/2014, 02:20

... applications of integer order differential equations wit h deviat ed arguments, we refer the reader to the refer- ences [39-45]. As far as we know, fractional order differential equations with ... some nonlinear ordinary differential equations with advanced arguments. Nonlinear Anal 2003, 53:495-505. 40. Yan JR: Oscillation of first- order impulsive differential equations with advanced ... Difference Equations 2011, 2011:2 http://www.advancesindifferenceequations.com/content/2011/1/2 Page 6 of 11 44. Wang G, Zhang L, Song G: Integral boundary value problems for first order integro-differential...

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... extended in several directions. First of all, it could be of interest to study the same kind of hierarchical classification A Hierarchical Classification of First- Order Recurrent Neural Networks ... Hierarchical Classification of First- Order Recurrent Neural Networks 151 hierarchy is actually a well-ordering. In fact, the RNN hierarchy consists of an alternating succession of non-self-dual and ... the issue of the expressive power of neural networks is approached from the point of view of the theory of automata on infinite words, and it is proved that first -order recurrent neural 1 More precisely,...

Ngày tải lên: 28/04/2014, 10:06

... class of higher -order difference equations Huantao Zhu 1 and Weibing Wang ∗2 1 Hunan College of Information, Changsha, Hunan 410200, P.R. China 2 Department of Mathematics, Hunan University of Science ... existence of periodic solutions for first -order functional difference equations [8–12]. Only a few article have been published on the same problem for higher -order functional difference equations. ... solutions of functional discrete systems and population model. Adv. Differ. Equ. 2005, 369–380 (2005) [13] Liu, Y: Periodic solutions of second order nonlinear functional difference equations. Archivum...

Ngày tải lên: 18/06/2014, 22:20

... decay of solutions for a quaslinear system of viscoelastic equations. Nonlinear Anal. 71, 2257–2267 (2009). doi:10.1016/j.na.2009.01.060 22. Agre, K, Rammaha, MA: Systems of nonlinear wave equations ... p. Next we want to derive the decay rate of energy function for problem (1.1). By mul- tiplying the first equation of system (1.1) by u and the second equation of system (1.1) by v, integrating over ... ∇u t ( t )) +2 ( ∇v ( t ) , ∇v t ( t )) +2β for a.e. t ∈ [0, T] . Multiplying the first equation of system (1.1) by u and the second equation of system (1.1) by v, integrating over Ω, using integration by parts...

Ngày tải lên: 21/06/2014, 00:20

... integration of nonlinear dynamic equations, ” Advances in Difference Equations, vol. 2008, Article ID 739602, 17 pages, 2008. 15 T. S. Hassan, “Oscillation of third order nonlinear delay dynamic equations ... class of second -order Emden-Fowler delay dynamic equations on time scales,” Journal of Mathematical Analysis and Applications, vol. 334, no. 2, pp. 847–858, 2007. 13 Y. S¸ahiner, “Oscillation of ... Advances in Difference Equations 9 M. Bohner, B. Karpuz, and ¨ O. ¨ Ocalan, “Iterated oscillation criteria for delay dynamic equations of first order, ” Advances in Difference Equations, vol. 2008,...

Ngày tải lên: 21/06/2014, 05:20

... “Existence of solutions for a class of third -order nonlinear boundary value problems,” Journal of Mathematical Analysis and Applications, vol. 294, no. 1, pp. 104–112, 2004. 14 D. Guo, Semi-Ordered ... solutions of nonlinear singular third -order two-point boundary value problem,” Journal of Mathematical Analysis and Applications, vol. 323, no. 1, pp. 413–425, 2006. 12 Y. Sun, “Positive solutions of ... singular boundary value problem of third -order differential equations, ” Mathematica Slovaca, vol. 60, no. 4, pp. 485–494, 2010. 4 Y. Sun, “Positive solutions for third -order three-point nonhomogeneous...

Ngày tải lên: 21/06/2014, 05:20

... ∪NRV 2 . Proof . First we show the last part of the statement. Let {x, y}be a fundamental set of solutions of 1.1,withy ∈NRV 1 , x ∈NRV 2 ,andletz be an arbitrary solution of 1.1,with z k > ... sequences and second order difference equations, ” Journal of Difference Equations and Applications, vol. 14, no. 1, pp. 17–30, 2008. 7 J. Jaro ˇ s and T. Kusano, “Self-adjoint differential equations and ... properties of Emden-Fowler difference equations, ” Central European Journal of Mathematics , vol. 7, no. 2, pp. 322–334, 2009. 13 P. ˇ Reh ´ ak, “Oscillatory properties of second order half-linear...

Ngày tải lên: 21/06/2014, 11:20

... economics. The theory of impulsive differential equations has become an important area of investigation in the recent years and is much richer than the corresponding theory of differential equations. For ... investigate the existence of minimal nonnegative solution for a class of second -order nonlinear impulsive differential equations on an infinite interval with an infinite number of impulsive times. Consider ... second- order impulsive differential equations, ” Journal of Computational and Applied Mathematics, vol. 223, no. 1, pp. 438–448, 2009. 24 J. Yan, “Existence of positive periodic solutions of impulsive...

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