solution of differential equation first order
Báo cáo hóa học: " Positive periodic solution of higher-order functional difference equation" ppt
... 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, 2011:56http://www.advancesindifferenceequations.com/content/2011/1/56Page 8 of 8 RESEARC H Open AccessPositive periodic solution of higher -order functional difference equation Mei-Lan ... k, , m ẻ N where Ndenotes 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...
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báo cáo hóa học: " Weak solutions of functional differential inequalities with first-order partial derivatives" ppt
... 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 infinitesystems 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 fromKamont Journal of Inequalities...
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báo cáo hóa học: " Some new results for BVPs of first-order nonlinear integro-differential equations of volterra type" doc
... new results for BVPs of first- order nonlinearintegro -differential equations of volterra typeYepeng Xing*and Yi Fu* Correspondence: ypxing-jason@hotmail.comDepartment of Mathematics,Shanghai ... University,200234, People’s Republic of ChinaAbstractIn 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, letx be a solution of (3.14). Note that x is also a solution of...
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Báo cáo hóa học: "Research Article Iterative Solutions of Singular Boundary Value Problems of Third-Order Differential Equation" potx
... “Existence of solutions for a class of third -order nonlinear boundary valueproblems,” 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...
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Báo cáo hóa học: " Research Article The Existence of Positive Solution to a Nonlinear Fractional Differential Equation with Integral Boundary Conditions" potx
... Difference Equations 136. ConclusionsIn 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 5Therefore, the unique solution of BVP 2.1 isxt −1Γαt0t ... and E. Mboumi, “Positive solutions of a boundary value problem for a nonlinearfractional differential equation, ” Electronic Journal of Qualitative Theory of Differential Equations,no.3,pp. 1–11,...
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Báo cáo hóa học: " Research Article Positive Solution of Singular Boundary Value Problem for a Nonlinear Fractional Differential Equation" potx
... existence of maximal and minimal solutions for 1.2.Definition 4.1. Let mt be a solution of 1.2 in 0, 1, then mt is said to be a maximal solution of 1.2, if for every solution ut of 1.2 ... fractionaldifferential equations have been of great interest, and there have been many resultson existence and uniqueness of the solution of boundary value problems for fractionaldifferential equations, ... Journal of Differential Equations , vol. 36, pp. 1–12, 2006.8 Z. B. Bai and H. S. Lău, Positive solutions for boundary value problem of nonlinear fractionaldifferential equation, ” Journal of Mathematical...
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báo cáo hóa học:" Research Article Biorthogonal Systems Approximating the Solution of the Nonlinear Volterra Integro-Differential Equation" doc
... 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 {ti}i≥1 of distinct points in 0, 1 andlet Tnbe the set {t1, ,tn} ordered in an ... used in order to establish the fact that the sequence defined inTheorem 3.1 approximates the solution of the nonlinear Volterra integro-differential equation, as well as giving an upper bond of the...
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Tài liệu Numerical Solution of Stochastic Differential Equations with Jumps in Finance pdf
... thusenhancing 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-algebraAfiltrationE(X) expectation of XE(X |A) conditional expectation of X under AP (A) probability of AP (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 learnsabout powerful numerical methods for the solution...
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A Hierarchical Classification of First-OrderRecurrent Neural Networks a10
... β>α.We now come up to the equivalence of the expressive power of recurrentneural networks and Muller automaton. First of all, we prove that any first- order recurrent neural network can be simulated ... specification of itsattr actors. Then there exists a Muller automaton ANsuch that L(N )=L(AN). A Hierarchical Classification of First- Order Recurrent Neural Networks 143class of rational-weighted ... obtained hierarchical classification of neural net-works consists of a decidable pre-well ordering of width 2 and height ωω,andadecidability procedure of this hierarchy is provided. Notably,...
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A Hierarchical Classification of First-OrderRecurrent Neural Networks cs12
... Wadge hierarchies of the class of all Σ11-sets.1The 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)0ωproduces an output of the form 0∗r((pb−1(k), qb−1(k)))0ω.Proof. A straightforward generalization of the proof of Lemma 2. The next result now shows that any Σ11-set of {0, 1}ωcan ... complexity of ω-languages [32]. Indeed, the Wadge hierarchy provides an extensive refinement of the Borelhierarchy, and hence permits a closer analysis of the topological complexity of classes of ω-languages....
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a hierarchical classification of first-order
... 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 151hierarchy is actually a well-ordering. In fact, the RNN hierarchy consists of analternating succession of non-self-dual and ... the issue of the expressivepower 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 neural1More precisely,...
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Báo cáo toán học: " Minimal and maximal solutions to first-order differential equations with state-dependent deviated arguments" pptx
... compact set of fixedpoints 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, itis a solution of (1) in [α, β]. First, ... prove that all solutions x of (4) obey x ≤ β on I.Claim3: The set of solutions of problem (1) in[α, β]has maximal andminimal elements. The setS = {x ∈ C(I) : x is a solution of (1) , x ∈ ... arbitrary solution of problem (10) andlet us prove that ˆx is neither the least nor the greatest solution of (10) in[α, β]. First, if ˆx changes sign in I0then ˆx cannot be an extremal solution of...
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báo cáo hóa học: " Existence and multiplicity of positive solutions for a nonlocal differential equation" docx
... 2011:5http://www.boundaryvalueproblems.com/content/2011/1/5Page 7 of 11 Then, Equation 12 holds.Therefore, by Equations 10 and 12 and the first part of Lemma 2.3, T has a fixedpoint inP ∩(¯2\1), which is a positive solution of Equation ... doi:10.1016/S0362-546X(01)00478-33. Kang, P, Wei, Z: Three positive solutions of singular nonlocal boundary value problems for systems of nonlinearsecond -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...
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báo cáo hóa học:" Research Article Nonoscillation of First-Order Dynamic Equations with Several Delays" pdf
... theorems on oscillation and nonoscillation of solutions to 1.3 are obtained. Thus, solutions of two different equations and/or twodifferent 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 timescales,” http://arxiv.org/abs/1001.0737v3 .6 M. Bohner, “Some oscillation criteria for first order delay dynamic equations,”...
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báo cáo hóa học:" Research Article Uniqueness and Parameter Dependence of Positive Solution of Fourth-Order Nonhomogeneous BVPs" pptx
... a unique solution and then studied the dependence of this solution on the parametersλ and μ.Sun11 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 BVPsJian-Ping Sun and Xiao-Yun WangDepartment of Applied Mathematics, Lanzhou University of Technology, Lanzhou, ... uniqueness of a positive solution. Thedependence of the solution on the parameters λii 1, 2, 3, 4 is also studied.1. IntroductionBoundary value problems BVPs for short consisting of fourth-order...
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