applications of linear differential equation of first order

... known, they found applications in the theory of first- order partial differential equations, including questions such as estimates of solutions of initial problems, estimates of domains of solutions, ... 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 ... functional differential inequalities generated by the Cauchy problem for nonlinear first- order partial functional differential equations. The unknown function is the functional variable in equation

Ngày tải lên: 21/06/2014, 02:20

... Equations 2011, 2011:14 http://www.advancesindifferenceequations.com/content/2011/1/14 RESEARCH Open Access Some new results for BVPs of first- order nonlinear integro -differential equations of ... -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 ... problem for first order integro -differential equation of Volterra type on time scales Nonlinear Anal 60, 429–442 (2005) Xing, Y, Ding, W, Han, M: Periodic boundary value problems of integro-differential

Ngày tải lên: 21/06/2014, 02:20

... f differential equations of tria n g u la r fo r m and those, o f truncated differential equations I Introduction Let us consider in a given separable Hilbert space // differential equations of ... study the asymt.ofcic equivalence of a class of differential equations i l l the Hilbert space H We will establish conditions for which the st udy of the asymptotic equivalence of (1) and (1) ... conditions of global theorem on the existence and uniqueness of solutions (see e.g p 187-189]) An interesting problem studied in the qualitative theory of solutions of ordinary differential equations

Ngày tải lên: 14/12/2017, 19:52

... Eq ⇔ xy2 dx − x1 dy = which is exact The solution is Linear Equations dx x y x = x2 = C 4.1 Definition A first- order linear differential equation has the form y + p(x)y = q(x) Example Looking ... Eq ⇔ xy2 dx − x1 dy = which is exact The solution is Linear Equations dx x y x = x2 = C 4.1 Definition A first- order linear differential equation has the form y + p(x)y = q(x) v dI R E Example ... Eq ⇔ xy2 dx − x1 dy = which is exact The solution is Linear Equations dx x y x = x2 = C 4.1 Definition A first- order linear differential equation has the form y + p(x)y = q(x) v dI R E Example

Ngày tải lên: 23/04/2020, 08:00

... Classification of First- Order Recurrent Neural Networks 143 class of rational-weighted first -order recurrent neural networks made up of Mc- Culloch and Pitts cells, and provide a refined classification of the ... 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 ... 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, 10:06

... 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 ... Proof The proof is similar to that of Theorem 4.13 We give the following example as an application of Theorem... 600 800 1000 1200 Figure 2: The graph of 7 iterates for the solutions of ... 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

Ngày tải lên: 21/06/2014, 11:20

... 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 Applications, ... 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,” ... oscillation of all solutions of first -order delay dynamic equations on arbitrary time scales, hence combining and extending results for corresponding differential and difference equations Examples, some of

Ngày tải lên: 22/06/2014, 11:20

... STABILITY OF PERIODIC SOLUTIONS OF FIRST- ORDER DIFFERENCE EQUATIONS LYING BETWEEN LOWER AND UPPER SOLUTIONS ALBERTO CABADA, VICTORIA ... Introduction It is well known that one of the most important concepts in the qualitative theory of dif- ferential and difference equations is the stability of the solutions of the treated problems. Classical ... Classical tools, as approximation by linear equations or Lyapunov functions, have been developed for both type of equations, see [7] for ordinary differential equations and [8] for difference ones.

Ngày tải lên: 23/06/2014, 00:20

... first- order branch WBbm g Woody biomass of a first- order branch TBbm g Total (foliage and woody) biomass of a first- order branch BH cm Height of the base of a first- order branch RBH Ratio of the ... of the height of the base of a first- order branch to tree height BE cm year –1 Elongation of a first- order branch per year FBbmI g year –1 Increment in foliar biomass of a first- order branch per ... terms of tree height per year B year –1 Birth rate of first- order branches per tree per year D year –1 Death rate of first- order branches per tree per year ∆ N year –1 Change in first- order branch

Ngày tải lên: 08/08/2014, 14:22

... 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 ... constant; here we have made use of the definitions of α i ,ρ i in 1.5, 1.7,and2p − q  1. Equation 3.8 is a second -order linear difference equation with two known linear independent solutions. ... 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

Ngày tải lên: 21/06/2014, 11:20

... introduction of the basic theory of impulsive differential equations, see Lakshmikantham et al ; for an overview of existing results and of recent research areas of impulsive differential equations, ... Article Positive Solutions of nth -Order Nonlinear Impulsive Differential Equation with Nonlocal Boundary Conditions Meiqiang Feng,1 Xuemei Zhang,2 and Xiaozhong Yang2 School of Science, Beijing Information ... problems,” Nonlinear Analysis Theory, Methods & Applications, vol 67, no 6, pp 1704–1709, 2007 40 R Ma and H Wang, “On the existence of positive solutions of fourth -order ordinary differential equations,”

Ngày tải lên: 21/06/2014, 16:20

... for a nonlinear hybrid differential equation of fractional order via regular Mittag–Leffler kernel Ibrahim Slimane1 | Zoubir Dahmani1 | Juan J Nieto2 | Thabet Abdeljawad3,4,5 Faculty of Exact ... continuous Applying the Proof Suppose that y is solution of (1), then by the above definition, we state that gðt,yðtÞÞ ABC fractional derivative of order α, we retrieve the first equation in (1) Replacing ... hybrid differential equations with fractional order Adv Differ Equ 2015;2015:183 https://doi.org/10.1186/s13662-015-0530-7 22 Jarad F, Abdeljawad T, Hammouch Z On a class of ordinary differential equations

Ngày tải lên: 29/03/2021, 16:41

... 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) ... inequalities for a class of even -order differential equations Qi-Ming Zhang∗1 and Xiaofei He2 College of Science, Hunan University of Technology, Zhuzhou, Hunan 412000, P.R China College of Mathematics ... improvements and generalizations of (1.2) in some literatures Especially, Lyapunov inequality has been generalized extensively to the higher -order linear equations and the linear Hamiltonian systems

Ngày tải lên: 20/06/2014, 21:20

... Difference Equations 13 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 ... & Applications, vol 69, no 8, pp 2677–2682, 2008 V Daftardar-Gejji, “Positive solutions of a system of non-autonomous fractional differential equations,” Journal of Mathematical Analysis and Applications, ... differential equations,” Journal of Mathematical Analysis and Applications, vol 345, no 2, pp 754–765, 2008 10 B Ahmad and J J Nieto, “Existence and approximation of solutions for a class of nonlinear

Ngày tải lên: 21/06/2014, 05:20

... class of four-point nonlocal boundary value problem of nonlinear integrodifferential equations of fractional order by applying some fixed point theorems On the other hand, impulsive differential equations ... of our knowledge, this is the first time in the literatures that a nonlocal boundary value problem of impulsive differential equations of fractional order is considered Advances in Difference Equations ... sciences, involves derivatives of fractional order Fractional differential equations also provide an excellent tool for the description of memory and hereditary properties of many materials and processes

Ngày tải lên: 21/06/2014, 07:20

... and Y Luchko, “Invariance of a partial differential equation of fractional order under the Lie group of scaling transformations,” Journal of Mathematical Analysis and Applications, vol 227, no ... notions of the fractional calculus and the theory of the operators for integration and differentiation of fractional order Section is devoted to the study of the existence and uniqueness of positive ... Electronic Journal of Differential Equations, vol 36, pp 1–12, 2006 Z B Bai and H S Lu, “Positive solutions for boundary value problem of nonlinear fractional ă dierential equation, Journal of Mathematical

Ngày tải lên: 21/06/2014, 07:20

... Estimation of Solutions of Linear Differential Systems of Neutral Type with Constant Coefficients ˇ ´ J Bastinec,1 J Dibl´k,1, D Ya Khusainov,3 and A Ryvolova1 ı Department of Mathematics, Faculty of ... suggested to the study of stability and estimates of solutions of 1.1 Exponential Stability and Estimates of the Convergence of Solutions to Stable Systems First we give two definitions of stability to ... solution of 1.1 is exponentially stable in the metric C1 Estimates of Solutions in a General Case Now we will estimate the norms of solutions of 1.1 and the norms of their derivatives in the case of

Ngày tải lên: 21/06/2014, 11:20

... 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 ... differential equations, ”... B S Alghamdi, “Analytic approximation of solutions of the forced Duffing equation with integral boundary conditions, ” Nonlinear Analysis: Theory, Methods & Applications,

Ngày tải lên: 21/06/2014, 16:20

... Difference Equations Volume 2009, Article ID 143175, 14 pages doi:10.1155/2009/143175 Research Article On the Spectrum of Almost Periodic Solution of Second -Order Neutral Delay Differential Equations ... 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 ... that the number of basic frequencies of ˙x  ψx, t,x∈ R, is the same as that of basic frequencies of its unique solution. 2 Advances in Difference Equations The spectrum containment of almost periodic

Ngày tải lên: 21/06/2014, 20:20

... theory of torsors, of this weaker statement). Let K be the Picard-Vessiot extension of a scalar differential equation L(y)=0 of order n over k.LetG be the differential Galois group of the equation ... translates into Z L =(r a,b )G L . 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 ... as u = y  y where y is a solution of Ly = 0. The element u itself satisfies a non linear equation of order d − 1. This equation is called the Riccati equation of L and has the form P d + a d−1 P d−1 +...

Ngày tải lên: 31/03/2014, 15:56