tackling systems of first order linear differential equations
báo cáo hóa học:" Research Article Error Bounds for Asymptotic Solutions of Second-Order Linear Difference Equations II: The First Case" pot
Ngày tải lên :
21/06/2014, 11:20
... second -order linear difference equations, ” Journal of Computational and Applied Mathematics, vol 41, no 1-2, pp 65–94, 1992 R Wong and H Li, “Asymptotic expansions for second -order linear difference equations ... bound of any solution for the “summary equation” 2.1 Next we consider a nonlinear first -order difference equation 6 Advances in Difference Equations 2.2 The Bound Estimate of a Solution to a Nonlinear ... inhomogeneous second -order linear difference equation; its solution takes the form of a particular solution added to an arbitrary linear combination of solutions to the associated homogeneous linear difference...
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Báo cáo sinh học: " Research Article Multiple Positive Solutions of Fourth-Order Impulsive Differential Equations with Integral Boundary Conditions and One-Dimensional p-Laplacian" ppt
Ngày tải lên :
21/06/2014, 16:20
... < ξ < L 3.27 Proof If 3.1 of H3 holds, similar to the proof of 3.7 , we can prove that Ty PC1 ≤ y PC1 y ∈ K, , y l PC1 3.28 If 3.14 and 3.15 of H4 hold, similar to the proof of 3.23 , we have ... solution y t , t ∈ J with property 3.17 Proof The proof is similar to that of Theorem 3.2 of Theorem 3.5 Assume that H1 , H2 , 3.1 of H3 and 3.14 and 3.15 of H4 hold In addition, letting f and Ik ... “Existence of solutions for impulsive integral boundary value problems of fractional order, ” Nonlinear Analysis: Hybrid Systems, vol 4, no 1, pp 134–141, 2010 D D Ba˘nov and P S Simeonov, Systems...
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Báo cáo hóa học: " Research Article On Periodic Solutions of Higher-Order Functional Differential Equations" ppt
Ngày tải lên :
21/06/2014, 22:20
... to one of the conditions of the lemma, admits estimate 2.18 Therefore, estimate 2.31 is valid 10 Boundary Value Problems Proof of the main results Proof of Theorem 1.1 Without loss of generality, ... Degree, and Nonlinear Differential Equations, vol 56 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1977 L A Kipnis, “On periodic solution of higher order nonlinear differential equations, ” ... solutions of higher order systems, ” Pacific Journal of Mathematics, vol 84, no 2, pp 275–282, 1979 G T Gegelia, “On boundary value problems of periodic type for ordinary odd order differential equations, ”...
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TWO-POINT BOUNDARY VALUE PROBLEMS FOR HIGHER-ORDER LINEAR DIFFERENTIAL EQUATIONS WITH STRONG pdf
Ngày tải lên :
23/06/2014, 00:20
... differential equations of higher order, Georgian Mathematical Journal (2001), no 4, 791–814 [11] I T Kiguradze and B L Shekhter, Singular boundary value problems for second -order ordinary differential equations, ... two-point boundary value problems for systems of higherorder ordinary differential equations with singularities, Georgian Mathematical Journal (1994), no 1, 31–45 32 Linear BVPs with strong singularities ... is, u is a solution of problem (1.1), (1.2) Let us show that u is a solution of that problem in the case n = 2m + as well In view of (2.67), it suffices to prove that u(m) (b) = First we find an estimate...
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báo cáo hóa học: " Some new results for BVPs of first-order nonlinear integro-differential equations of volterra type" doc
Ngày tải lên :
21/06/2014, 02:20
... -x(1) The authors of [20-24] consider this kind of “anti-periodic” conditions for differential equations or impulsive differential equations To the best of our knowledge it is the first article to ... integro -differential equations of Volterra type on time scales Nonlinear Anal 68, 127–138 (2008) doi:10.1016/j.na.2006.10.036 Xu, H, Nieto, JJ: Extremal solutions of a class of nonlinear integro -differential equations ... article as: Xing and Fu: Some new results for BVPs of first- order nonlinear integro -differential equations of volterra type Advances in Difference Equations 2011 2011:14 Submit your manuscript to...
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galois theory of linear differential equations - m. van der put, m. singer
Ngày tải lên :
31/03/2014, 15:56
... of the derivations of L/k that commute with the derivation on L (3) The field LG of G-invariant elements of L is equal to k Proof An intuitive proof of (1) and (2) L is the field of fractions of ... isomorphism translates into ZL = (ra,b )GL A proof of Lemma 1.29 finishes the proof of the theorem Proof of lemma 1.29 The proof is rather similar to the one of lemma 1.23 The only thing that we have ... help of Exercise 1.5.3, that the dimension of the F -vector space Der(F/C) is equal to d 1.2 Linear Differential Equations Let k be a differential field with field of constants C Linear differential equations...
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báo cáo hóa học:" Research Article Nonoscillation of First-Order Dynamic Equations with Several Delays" pdf
Ngày tải lên :
21/06/2014, 11:20
... 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 M Bohner, “Some oscillation criteria for first order delay dynamic equations, ” ... The Rocky Mountain Journal of Mathematics, vol 38, no 1, pp 1–18, 2008 11 Y Sahiner and I P Stavroulakis, “Oscillations of first order delay dynamic equations, ” Dynamic ¸ Systems and Applications,...
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Báo cáo sinh học: " Research Article Existence and Lyapunov Stability of Periodic Solutions for Generalized Higher-Order Neutral Differential Equations" potx
Ngày tải lên :
21/06/2014, 16:20
... second -order neutral functional differential equations, ” Journal of Mathematical Analysis and Applications, vol 329, no 1, pp 677–689, 2007 10 M R Zhang, “Periodic solutions of linear and quasilinear ... periodic solutions of nonlinear neutral functional differential equations, ” Nonlinear Analysis: Real World Applications, vol 9, no 3, pp 977–984, 2008 K Wang and S Lu, “On the existence of periodic solutions ... In general, most of the existing results are concentrated on lower -order neutral functional differential equations, while studies on higher -order neutral functional differential equations are rather...
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Báo cáo hóa học: " Research Article Sturm-Picone Comparison Theorem of Second-Order Linear Equations on Time Scales" ppt
Ngày tải lên :
21/06/2014, 20:20
... differential equations of second order, ” Annals of Mathematics, vol 65, pp 197–202, 1957 R Zhuang, “Sturm comparison theorem of solution for second order nonlinear differential equations, ” Annals of Differential ... for linear differential equations of second order, ” Proceedings of the American Mathematical Society, vol 13, pp 603–610, 1962 W Leighton, “Some elementary Sturm theory,” Journal of Differential Equations, ... theorem of second -order linear differential equations 1.3 Sturm-Picone Comparison Theorem Assume that x t and y t are the nontrivial solutions of 1.3 and a, b are two consecutive zeros of x t...
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Báo cáo hóa học: " Research Article Iterated Oscillation Criteria for Delay Dynamic Equations of First Order" pdf
Ngày tải lên :
22/06/2014, 11:20
... criterion for first order dynamic equations, ” to appear in Functional Differential Equations 10 Y Sahiner and I P Stavroulakis, “Oscillations of first order delay dynamic equations, ” Dynamic ¸ Systems and ... criteria for first order delay dynamic equations, ” Far East Journal of Applied Mathematics, vol 18, no 3, pp 289–304, 2005 B G Zhang and X Deng, “Oscillation of delay differential equations on time ... of delay differential equations, ” Journal of Mathematical Analysis and Applications, vol 219, no 1, pp 165–178, 1998 J Shen and X Tang, “New oscillation criteria for linear delay differential equations, ”...
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Báo cáo hóa học: " Research Article On Complex Oscillation Property of Solutions for Higher-Order Periodic Differential Equations Zong-Xuan Chen and Shi-An Gao" pdf
Ngày tải lên :
22/06/2014, 18:20
... that f1 and f2 are linearly dependent We remark that the above proof remains valid if we interchange the roles of G j and g j as at the end of the proof of Lemma 2.6 The proof of Theorem 1.3 is ... every solution f ≡ of (1.2) satisfies (1.14) This completes the proof of Theorem 1.6 Proofs of corollaries Proof of Corollary 1.4 By Remark 2.7, we see that the hypotheses of Theorem 1.3 are satisfied ... function N1 (ρ,1/G) of G(ξ) in < |ξ | < ∞ satisfies log+ N1 (ρ,1/G) = O(logρ) So that u(ξ) is an entire function of finite order Secondly, we prove that h(ξ) is of finite order of growth Set W(ξ)...
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STABILITY OF PERIODIC SOLUTIONS OF FIRST-ORDER DIFFERENCE EQUATIONS LYING BETWEEN LOWER AND UPPER pptx
Ngày tải lên :
23/06/2014, 00:20
... optimality of the obtained results Preliminaries This paper is devoted to study the stability, by using the method of lower and upper solutions, of the N-periodic solutions of the following first -order ... see [1, 2], that the existence of α and β, a pair of lower and upper solutions of problem (PN ), such that α ≤ β in JN , does not imply the existence of a solution of this problem Alberto Cabada ... more precise description of the set of solutions of problem (PN ) Lemma 2.5 Assume conditions (H) and (H f ) Let u, v ∈ [α,β] be two solutions of problem (PN ) Then, one of the following statements...
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a hierarchical classification of first-order
Ngày tải lên :
28/04/2014, 10:06
... Classification of First- Order Recurrent Neural Networks 143 class of rational-weighted first -order recurrent neural networks made up of McCulloch and Pitts cells, and provide a refined classification of the ... The obtained hierarchical classification of neural networks consists of a decidable pre-well ordering of width and height ω ω , and a decidability procedure of this hierarchy is provided Notably, ... irrespective of the fact that this sequence is periodic or not, some state will repeat finitely often whereas other will repeat infinitely often The (finite) set of states occurring infinitely often in...
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báo cáo hóa học:" Periodic boundary value problems for nonlinear first-order impulsive dynamic equations on time scales" pot
Ngày tải lên :
21/06/2014, 17:20
... for nonlinear first -order impulsive dynamic equations on time scales Da-Bin Wang Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050, People’s Republic of China ... 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 ... differential equations is emerging as an important area of investigation, since it is a lot richer than the corresponding theory of differential equations without impulse effects Moreover, such equations...
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Báo cáo hóa học: " Research Article Global Behavior of Solutions to Two Classes of Second-Order Rational Difference Equations Sukanya Basu and Orlando Meri" docx
Ngày tải lên :
21/06/2014, 20:20
... solutions m, M ∈ L, U of either one of the systems of equations M f M, M , m f m, m , M f m, m , m f M, M 3.6 and 3.7 necessarily satisfy m M In either case, the hypotheses i or ii of Theorem 2.1 are ... completes the proof of the lemma Proof of Theorem 1.4 To prove Theorem 1.4 it is enough to assume statement B of Proposition 3.1 Also by Lemma 3.3 we may assume p / q without loss of generality ... the proof of Theorem 1.4 By considering the restriction of the map T of 1.15 to m∗ , M∗ , an application of the Schauder Fixed Point Theorem 17 gives that m∗ , M∗ contains the fixed point of T ,...
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Báo cáo hoa học: " Research Article Multiple Positive Solutions for Nonlinear First-Order Impulsive Dynamic Equations on Time Scales with Parameter" ppt
Ngày tải lên :
21/06/2014, 20:20
... difference equations with impulses,” International Journal of Difference Equations, vol 1, no 2, pp 225–239, 2006 15 Y Li, X Fan, and L Zhao, “Positive periodic solutions of functional differential equations ... periodic problems of first order, ” Journal of Mathematical Analysis and Applications, vol 205, no 2, pp 423–433, 1997 17 J J Nieto, “Impulsive resonance periodic problems of first order, ” Applied ... Electronic 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 on...
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Báo cáo hoa học: " Research Article On Connection between Second-Order Delay Differential Equations and Integrodifferential Equations with Delay" pdf
Ngày tải lên :
21/06/2014, 20:20
... ψ is 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, we ... equation while in a second -order equation is reduced to a system of a nonlinear inequality and a linear delay equation Similar in a sense problems for delay difference equations were studied in ... Advances in Difference Equations One of the methods used to study 1.1 is transforming the second -order delay differential equation to a first -order differential or integrodifferential equations with delay...
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Báo cáo hóa học: " Research Article New Results on Multiple Solutions for Nth-Order Fuzzy Differential Equations under Generalized Differentiability" ppt
Ngày tải lên :
21/06/2014, 20:20
... different approaches to the solvability of Nth -order linear fuzzy differential equations Here, using the concept of generalized derivative and its extension to higher -order derivatives, we show that we ... case of fN t differentiability, then f g is generalized differentiable of order N at t and f g N t N t (The sum of two functions is defined pointwise.) g Proof By Definition 3.2 the statement of the ... types to define higher -order derivatives of fuzzy-number-valued functions Then, we propose a new method to solve higher -order fuzzy differential equations based on the selection of derivative type...
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Báo cáo hóa học: " Research Article Dynamical Properties for a Class of Fourth-Order Nonlinear Difference Equations" potx
Ngày tải lên :
22/06/2014, 06:20
... of 3.12 , 3.13 , 3.17 , and 3.20 , we see that c is true The proofs of d and e are similar to those of c The proof for this lemma is complete Lemma 3.5 Let {xn }∞ −3 be a positive solution of ... York, NY, USA, 1992 V L Koci´ and G Ladas, Global Behavior of Nonlinear Difference Equations of Higher Order with Applicac tions, vol 256 of Mathematics and Its Applications, Kluwer Academic Publishers, ... Proof By Lemma 3.4 a , one can see that the length of a negative semicycle is at most 4, and that of a positive semicycle is at most On the basis of the strictly oscillatory character of the...
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