solution of differential equation first order

... 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 ... k, , m ẻ N where N denotes the set of positive integers. The purpose of this article is to consider the existence of positive periodic solution of higher -order functional differen ce equatio...

Ngày tải lên: 20/06/2014, 22:20

... of first- order partial differential equations, including questions such as estimates of solutions of initial problems, estimates of domains of solutions, estimates of the difference between solutions ... infinite systems of differential functional equations and strongly coupled infinite systems of first order partial differential equations. Rocky Mt J Math. 10, 237–246 (1980) Kamont Journal of Inequalities ... c]. Proof The existence and uniqueness of the solution to (30) follows from classical the- orems on Carathéodory solutions of ordinary differential equations. We conclude from Kamont Journal of Inequalities...

Ngày tải lên: 21/06/2014, 02:20

... 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

... “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 ... problem,” Journal of Mathematical Analysis and Applications, vol. 323, no. 1, pp. 413–425, 2006. 12 Y. Sun, “Positive solutions of singular third -order three-point boundary value problem,” Journal of Mathematical ... 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

... 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

... existence of maximal and minimal solutions for 1.2. Definition 4.1. Let mt be a solution of 1.2 in 0, 1, then mt is said to be a maximal solution of 1.2, if for every solution ut of 1.2 ... fractional differential equations have been of great interest, and there have been many results on existence and uniqueness of the solution of boundary value problems for fractional differential equations, ... Journal of Differential Equations , vol. 36, pp. 1–12, 2006. 8 Z. B. Bai and H. S. L ă u, Positive solutions for boundary value problem of nonlinear fractional differential equation, ” Journal of Mathematical...

Ngày tải lên: 21/06/2014, 07:20

... in order to approximate the solution of the nonlinear Volterra integro-differential equation. We define, following a fixed-point approach, a sequence of functions which approximate the solution of ... estimate the rate of convergence of the sequence of projections. For this purpose, consider the dense subset {t i } i≥1 of distinct points in 0, 1 and let T n be the set {t 1 , ,t n } ordered in an ... used in order to establish the fact that the sequence defined in Theorem 3.1 approximates the solution of the nonlinear Volterra integro-differential equation, as well as giving an upper bond of the...

Ngày tải lên: 21/06/2014, 10:20

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Ngày tải lên: 21/06/2014, 20:20

... thus enhancing the order of strong convergence from γ =0.5toγ =1.0. Nonethe- less, the order of weak convergence of the Milstein scheme equals β =1.0, which is not an improvement over the order of weak ... collection of events, sigma-algebra A filtration E(X) expectation of X E(X |A) conditional expectation of X under A P (A) probability of A P (A |B) probability of A conditioned on B ∈ element of ∈ ... approxi- mation of continuous solutions of SDEs. The discrete time approximation of SDEs with jumps represents the focus of the monograph. The reader learns about powerful numerical methods for the solution...

Ngày tải lên: 19/02/2014, 22:20

... β>α. We now come up to the equivalence of the expressive power of recurrent neural networks and Muller automaton. First of all, we prove that any first- order recurrent neural network can be simulated ... specification of its attr actors. Then there exists a Muller automaton A N such that L(N )=L(A N ). A Hierarchical Classification of First- Order Recurrent Neural Networks 143 class of rational-weighted ... obtained hierarchical classification of neural net- works consists of a decidable pre-well ordering of width 2 and height ω ω ,anda decidability procedure of this hierarchy is provided. Notably,...

Ngày tải lên: 28/04/2014, 09:49

... Wadge hierarchies of the class of all Σ 1 1 -sets. 1 The Wadge hierarchy of a given class of ω-languages corresponds to the collection of all ω-languages of this class ordered by the Wadge reduction ... 2 −k )0 ω produces an output of the form 0 ∗ r((p b −1 (k) , q b −1 (k) ))0 ω . Proof. A straightforward generalization of the proof of Lemma 2.  The next result now shows that any Σ 1 1 -set of {0, 1} ω can ... complexity of ω-languages [32]. Indeed, the Wadge hierarchy provides an extensive refinement of the Borel hierarchy, and hence permits a closer analysis of the topological complexity of classes of ω-languages....

Ngày tải lên: 28/04/2014, 09:49

... 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

... 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, ... prove that all solutions x of (4) obey x ≤ β on I. Claim 3 : The set of solutions of problem (1) in [ α, β ] has maximal and minimal elements. The set S = {x ∈ C(I) : x is a solution of (1) , x ∈ ... arbitrary solution of problem (10) and let us prove that ˆx is neither the least nor the greatest solution of (10) in [α, β]. First, if ˆx changes sign in I 0 then ˆx cannot be an extremal solution of...

Ngày tải lên: 20/06/2014, 20:20

... 2011:5 http://www.boundaryvalueproblems.com/content/2011/1/5 Page 7 of 11 Then, Equation 12 holds. Therefore, by Equations 10 and 12 and the first part of Lemma 2.3, T has a fixed point in P ∩ ( ¯  2 \ 1 ) , which is a positive solution of Equation ... doi:10.1016/S0362-546X(01)00478-3 3. Kang, P, Wei, Z: Three positive solutions of singular nonlocal boundary value problems for systems of nonlinear second -order ordinary differential equations. Nonlinear Anal. 70, 444–451 ... boundary value problems of arbitrary order. J Lond Math Soc. 79, 238–258 (2009) 9. Zhang, Z, Perera, K: Sign-changing solutions of Kirchhoff type problems via invariant sets of descent flow. J Math...

Ngày tải lên: 21/06/2014, 02:20

... 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

... 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 ... 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, ... uniqueness of a positive solution. The dependence of the solution on the parameters λ i i  1, 2, 3, 4 is also studied. 1. Introduction Boundary value problems BVPs for short consisting of fourth-order...

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Ngày tải lên: 21/06/2014, 11:20

Ngày tải lên: 21/06/2014, 11:20

Ngày tải lên: 21/06/2014, 11:20