general solution of first order homogeneous differential equation

... Most of these discrete mathematical 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 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 ... higher -order functional difference equations. In 2010, Wang and Chen [9] have studi ed the existence of positive periodic solutions for the following general higher -order functional difference equation x(n + m...

Ngày tải lên: 20/06/2014, 22:20

... introduction of the basic theory of impulsive differential equations, see Lakshmikantham et al. 1; for an overview of existing results and of recent research areas of impulsive differential equations, ... fourth -order beam equations,” Journal of Mathematical Analysis and Applications, vol. 270, no. 2, pp. 357–368, 2002. 42 R. Ma and H. Wang, “On the existence of positive solutions of fourth -order ... Article Multiple Positive Solutions of Fourth -Order Impulsive Differential Equations with Integral Boundary Conditions and One-Dimensional p-Laplacian Meiqiang Feng School of Applied Science, Beijing...

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Ngày tải lên: 21/06/2014, 22:20

... new results for BVPs of first- order nonlinear integro -differential equations of volterra type Yepeng Xing * and Yi Fu * Correspondence: ypxing- jason@hotmail.com Department of Mathematics, Shanghai ... University, 200234, People’s Republic of China Abstract In this work we present some new results concerning the existence of solutions for first- order nonlinear integro -differential equations with boundary ... potential solutions of x = λTx, λ ∈ [ 0, 1 ], (3:14) are bounded a priori, with the bound being independent of l. With this in mind, let x be a solution of (3.14). Note that x is also a solution of...

Ngày tải lên: 21/06/2014, 02:20

... 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 ... which guarantees the uniqueness of solution of 1.1 and cannot be omitted. To study the spectrum of almost periodic solution of 1.1, we firstly study the solution of 1.1.Let f 1 n   n1 n  s n f  σ  dσ ... 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...

Ngày tải lên: 21/06/2014, 20:20

... Difference Equations 13 6. Conclusions In this paper, by using the fixed point theorem of cone, we have investigated the existence of positive solutions for a class of nonlinear fractional differential equations ... preliminaries for discussing the existence of positive solutions of boundary value problem 1.5. Advances in Difference Equations 5 Therefore, the unique solution of BVP 2.1 is x  t   − 1 Γ  α   t 0  t ... and E. Mboumi, “Positive solutions of a boundary value problem for a nonlinear fractional differential equation, ” Electronic Journal of Qualitative Theory of Differential Equations,no.3, pp. 1–11,...

Ngày tải lên: 21/06/2014, 05:20

... l  j       3.11 are finite. Equation 3.10 is a inhomogeneous second -order linear difference equation; its solution takes the form of a particular solution added to an arbitrary linear combination of solutions ... constant. Equation 4.14 is an inhomogeneous second -order linear difference equation; its solution takes the form of a particular solution added to an arbitrary linear combination of solutions ... asymptotic solutions of second -order linear differential equations, the method used in Wong and Li’s papers cannot give us way to obtain error bounds of these asymptotic solutions. Only order estimations...

Ngày tải lên: 21/06/2014, 11:20

... theorems on oscillation and nonoscillation of solutions to 1.3 are obtained. Thus, solutions of two different equations and/or two different solutions of the same equation are compared, which allows ... 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,”...

Ngày tải lên: 21/06/2014, 11:20

... and Lyapunov Stability of Periodic Solutions for Generalized Higher -Order Neutral Differential Equations Jingli Ren, 1 Wing-Sum Cheung, 2 and Zhibo Cheng 1 1 Department of Mathematics, Zhengzhou ... stability of periodic solutions for a generalized higher -order neutral differential equation are established. 1. Introduction In recent years, there is a good amount of work on periodic solutions ... study the Lyapunov stability of the periodic solutions of 3.32. Theorem 3.5. Assume that H 4  holds. Then every T-periodic solution of 3.32 is Lyapunov stable. Proof. Let z 1  t   x  t  ,z 2  t  ...

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Ngày tải lên: 23/06/2014, 00:20

... 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

... 2011:46 http://www.advancesindifferenceequations.com/content/2011/1/46 Page 8 of 9 and either m = ∞ or m < ∞ and x m +1 < ¯ x . A negative semicycle of a solution { x n } ∞ n =− 1 of Equation (1.1) consists of a string of terms ... the solution is a nontrivial solution, then we can further divide the solution into two cases: non-oscillatory solution and oscillatory solution. A nontrivial solution {x n } ∞ n =− 1 of Equation ... negative. There do not e xist eventua lly positive non-oscillatory solutions of Equation (1.1). Proof. Consider a solution of Equation (1.1) with x −1 , x 0 ∈ ( 0, 1 ). We then know from Lemma...

Ngày tải lên: 20/06/2014, 22:20

... and Parameter Dependence of Positive Solution of Fourth -Order Nonhomogeneous BVPs Jian-Ping Sun and Xiao-Yun Wang Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, ... a unique solution and then studied the dependence of this solution on the parameters λ and μ.Sun11 discussed the existence and nonexistence of positive solutions to a class of third -order three-point ... dependence of solutions of second -order boundary value problems,” Applied Mathematics Letters, vol. 22, no. 11, pp. 1633–1638, 2009. 11 Y. Sun, “Positive solutions for third -order three-point nonhomogeneous...

Ngày tải lên: 21/06/2014, 11:20

... cone, in this article, some results of one and two positive solutions to a class of nonlinear first -order periodic boundary value problems of impulsive dynamic equations on time scales are obtained. Two ... S: Positive solutions for first order periodic boundary value problem. Appl. Math. Comput. 158, 345–351 (2004) [39] Sun, JP, Li, WT: Positive solution for system of nonlinear first -order PBVPs ... differential equations is emerging as an important area of in- vestigation, since it is a lot richer than the corresponding theory of differential equations without impulse effects. Moreover, such equations...

Ngày tải lên: 21/06/2014, 17:20

... global dynamics of 1.11 and 1.13, such as the character of the prime period-two solutions to either equation, or even for more general rational second -order equations, when such solutions exist. ... Article Global Behavior of Solutions to Two Classes of Second -Order Rational Difference Equations Sukanya Basu and Orlando Merino Department of Mathematics, University of Rhode Island, Kingston, ... completes the proof of the lemma. 5. Proof of Theorem 1.4 To prove Theorem 1.4 it is enough to assume statement B of Proposition 3.1.Alsoby Lemma 3.3 we may assume p /  q without loss of generality....

Ngày tải lên: 21/06/2014, 20:20

... 3.3 Advances in Difference Equations 9 14 J. Li and J. Shen, “Positive solutions for first order difference equations with impulses,” International Journal of Difference Equations, vol. 1, no. 2, ... Leggett-Williams fixed point theorem, the existence of three positive solutions to a class of nonlinear first -order periodic b oundary value problems of impulsive dynamic equations on time scales with parameter ... Journal of Qualitative Theory of Differential Equations, vol. 2005, no. 12, pp. 1–22, 2005. 21 M. Benchohra, J. Henderson, S. K. Ntouyas, and A. Ouahab, “On first order impulsive dynamic equations...

Ngày tải lên: 21/06/2014, 20:20

... defined by 2.5. Proof. In the proof we will use notation defined in the proof of Theorem 2.1. The existence and uniqueness of a solution of 1.11, 2.1 is a consequence of Theorem 2.1. Thus, ... second order delay equation is reduced to one first -order integrodifferential delay equation while in 2 a second -order equation is reduced to a system of a nonlinear inequality and a linear delay equation. Similar ... between Second -Order Delay Differential Equations and Integrodifferential Equations with Delay Leonid Berezansky, 1 Josef Dibl ´ ık, 2, 3 and Zden ˘ ek ˇ Smarda 3 1 Department of Mathematics,...

Ngày tải lên: 21/06/2014, 20:20

Ngày tải lên: 21/06/2014, 20:20