systems of ordinary differential equations examples

... Trang 1 Periodic solutions of some linear evolution systems of natural differential equations on 2-dimensional tore Dang Khanh Hoi* Department of General Education, Hoa Binh University, ... the linear differential equations on manifolds in which includes the external differential operators At research of such equations appear so named the small denominators, so such equations is ... bundle of manifolds X, C°(€) is the space of smooth differential forms and H*(€) is the Sobolev space of differential forms over X (see, [4]) By A we denote operator i(d+0), so-called natural differential

Ngày tải lên: 14/03/2014, 13:20

... ordinary differential equations Chapter PRELIMINARIES 1.1 Introduction In this thesis, we explore the stability of ordinary differential equations And we will consider differential equations in the ... set of x A(x) The α-limit set of x Γ Simple closed curve (or periodic orbit) T Period iv Bachelor thesis PHUNG THI HONG LIEN Preface Differential equations are one of the most important areas of ... instability of an orbit A more general method is the Lyapunov function In fact, any one of the numbers of different stabilization standards is used Therefore, we will study the stability of ordinary differential

Ngày tải lên: 23/12/2019, 16:17

... ordinary differential equations Chapter PRELIMINARIES 1.1 Introduction In this thesis, we explore the stability of ordinary differential equations And we will consider differential equations in the ... set of x A(x) The α-limit set of x Γ Simple closed curve (or periodic orbit) T Period iv Bachelor thesis PHUNG THI HONG LIEN Preface Differential equations are one of the most important areas of ... instability of an orbit A more general method is the Lyapunov function In fact, any one of the numbers of different stabilization standards is used Therefore, we will study the stability of ordinary differential

Ngày tải lên: 07/04/2021, 08:05

... to the study of weakly coupled elliptic systems of partial differential equations (see [] for weakly coupled systems) Such systems arise in financial mathematics and in the form of the so called ... Equations 2013, 2013:315 http://www.advancesindifferenceequations.com/content/2013/1/315 RESEARCH Open Access Feynman-Kac formula for switching diffusions: connections of systems of partial differential ... traditional differential equation models Dynamic systems mentioned above are often referred to as hybrid systems One of the representatives in the class of hybrid system is a switching diffusion process

Ngày tải lên: 04/12/2022, 10:35

... Proof. By the continuation of solutions and the singularity of ᏷ at the point P 0 , the set ᏷(P 0 ) = ∅. Taking into account the nature of the vector field and the definition of the singularit y of ... this paper as “the nature of the vec- tor field.” Therefore, a combination of properties of the associated vector field with the Kneser’s property of the cross sections of the solutions’ funnel ... TERMINAL VALUE PROBLEM FOR SINGULAR ORDINARY DIFFERENTIAL EQUATIONS: THEORETICAL ANALYSIS AND NUMERICAL SIMULATIONS OF GROUND STATES ALEX P. PALAMIDES AND THEODOROS G. YANNOPOULOS

Ngày tải lên: 22/06/2014, 22:20

... MATH 3036- DIFFERENTIAL EQUATIONS Lecturer : Dr Nguyễn Hữu Thọ Department of Mathematics - WRU Slide 11 - Unit Introduction to Differential Equations Dr Nguyen Huu Tho - Department of Mathematics ... Chapter Introduction to Differential Equations 1.1 Differential Equations Models Dr Nguyen Huu Tho - Department of Mathematics Slide 11 - Dr Nguyen Huu Tho - Department of Mathematics Slide 11 ... to solve Differential Equations Dr Nguyen Huu Tho - Department of Mathematics Slide 11 - 276 Dr Nguyen Huu Tho - Department of Mathematics Slide 11 - 277 Dr Nguyen Huu Tho - Department of Mathematics

Ngày tải lên: 16/12/2020, 00:10

... MATH 3036- DIFFERENTIAL EQUATIONS Lecturer : Dr Nguyễn Hữu Thọ Department of Mathematics - WRU Slide 11 - Unit Introduction to Differential Equations Dr Nguyen Huu Tho - Department of Mathematics ... Chapter Introduction to Differential Equations 1.1 Differential Equations Models Dr Nguyen Huu Tho - Department of Mathematics Slide 11 - Dr Nguyen Huu Tho - Department of Mathematics Slide 11 ... to solve Differential Equations Dr Nguyen Huu Tho - Department of Mathematics Slide 11 - 276 Dr Nguyen Huu Tho - Department of Mathematics Slide 11 - 277 Dr Nguyen Huu Tho - Department of Mathematics

Ngày tải lên: 21/03/2021, 18:30

... problems for systems of differential equations, ” Proceedings of the Royal Society of Edinburgh Section A, vol 78, no 1-2, pp 139–159, 1977 6 Y Liu and W Ge, “Positive periodic solutions of nonlinear ... doi:10.1155/2011/192156 Research Article Existence and Uniqueness of Periodic Solution for Nonlinear Second-Order Ordinary Differential Equations Jian Zu College of Mathematics, Jilin University, Changchun 130012, ... about the existence of periodic solutions for second-order differential equations have been obtained by combining the classical method of lower and upper solutions and the method of alternative problems

Ngày tải lên: 14/07/2023, 09:44

... made available soon. Further results of the estimate of growth of entire solutions of some classes of algebraic differential equations Advances in Difference Equations 2012, 2012:6 doi:10.1186/1687-1847-2012-6 ... this is a contradiction The proof of Theorem 1.4 is complete 13 Proof of Theorem 1.9 By the first equation of the systems of algebraic differential equations (1.4), we know (n) w1 ... Further results of the estimate of growth of entire solutions of some classes of algebraic differential equations Qi Jianming 1,3 , Li Yezhou 2 and Yuan Wenjun ∗3 1 Department of Mathematics and

Ngày tải lên: 20/06/2014, 20:20

... different classes of systems of nonlinear matrix equations involving Lipshitzian mappings. 2000 Mathematics Subject Classifications: 15A24; 65H05. Keywords: nonlinear matrix equations, Lipshitzian ... for the study of solutions to systems of nonlinear matrix equations involving contractive mappings. We first review the Thompson metric on the open convex cone P(n)(n ≥ 2), the set of all n×n Hermitian ... F: Positive defined solution of two kinds of nonlinear matrix equations. Surv Math Appl. 4, 179–190 (2009) 12. Hasanov, V: Positive definite solutions of the matrix equations X ± A*X -q A = Q.

Ngày tải lên: 20/06/2014, 22:20

... (4.6) we see that the analog of (3.15) holds □ In view of the proof of Theorem 4.2, we see that the proof of subsequent Theorems 4.3-4.5 will also be similar to that of Theorems 3.3-3.5 with the ... Difference Equations 2011, 2011:43 http://www.advancesindifferenceequations.com/content/2011/1/43 RESEARCH Open Access Existence results of Brezis-Browder type for systems of Fredholm integral equations ... solutions of some boundary value problems J Math Anal Appl 184, 640–648 (1994) doi:10.1006/jmaa.1994.1227 Erbe, LH, Wang, H: On the existence of positive solutions of ordinary differential equations

Ngày tải lên: 20/06/2014, 22:20

... asymptotic stability of the nonlinear impulsive stochastic differential equations and the impulsive stochastic partial differential equations with infinite delays by means of the fixed point theory ... College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, China Full list of author information is available at the end of the article Abstract The linear neutral differential ... Advances in Difference Equations 2011, 2011:48 http://www.advancesindifferenceequations.com/content/2011/1/48 RESEARCH Open Access New criteria for stability of neutral differential equations with variable

Ngày tải lên: 20/06/2014, 22:20

... Difference Equations 2011, 2011:10 http://www.advancesindifferenceequations.com/content/2011/1/10 RESEARCH Open Access Positive solutions for a coupled system of nonlinear differential equations of mixed ... School of Science, University of Jinan, Jinan 250022, Shandong, PR China Full list of author information is available at the end of the article Abstract In this article, we study the existence of ... this article, we study the existence of positive solutions for a coupled system of nonlinear differential equations of mixed fractional orders ⎧ ⎪ −Dα+ u(t) = f (t, v(t)), < t < 1, ⎨ β0 D0+ v(t)

Ngày tải lên: 21/06/2014, 03:20

... the use of Gronwall inequality Then, v ≤ u in DT , and the proof of part i of the lemma is completed The similar argument gives the proof of part ii of the lemma Advances in Difference Equations ... principle of induction, we complete the proof of the lemma Uniform Estimates of {um }, {um } To prove the existence of solutions to 1.1 , in this section, we show the uniform estimates of {um }, ... , and independent of m 0, Proof By Hypothesis H , 3.20 , and 3.27 , the proof similar to that of 15, Lemma 4.4 gives 3.31 , and, by 3.20 and 3.28 , the proof similar to that of 15, Lemma 4.3 gives

Ngày tải lên: 21/06/2014, 05:20

... coefficients of like powers of p, we get the following set of equations: coefficient of p0 : Y0 ∞ L−1 ai,n Pn t , 3.11 n coefficient of p1 : Y1 L−1 fi i L−1 Yi,1 − L−1 Ni Yi,0 i i Now, we solve these equations ... integer-order equations are found to follow as special cases of those of fractional-order equations We consider the system of fractional-order equations of the form Dαi yi t Fi t, y1 , y2 , y3 , , yn ... differential equations by extending the idea of 17, 18 This method leads to computable and efficient solutions to linear and nonlinear operator equations The corresponding solutions of the integer-order equations

Ngày tải lên: 21/06/2014, 05:20

... made available soon. Further results of the estimate of growth of entire solutions of some classes of algebraic differential equations Advances in Difference Equations 2012, 2012:6 doi:10.1186/1687-1847-2012-6 ... this is a contradiction The proof of Theorem 1.4 is complete 13 Proof of Theorem 1.9 By the first equation of the systems of algebraic differential equations (1.4), we know (n) w1 ... Further results of the estimate of growth of entire solutions of some classes of algebraic differential equations Qi Jianming 1,3 , Li Yezhou 2 and Yuan Wenjun ∗3 1 Department of Mathematics and

Ngày tải lên: 21/06/2014, 17:20

... appear in the study of systems with automatic regulation and automatic control of various technical systems It often occurs that the law of regulation depends on maximum values of some regulated ... Distribution of the zeros of the solutions of hyperbolic differential equations with maxima Rocky Mt J Math 37(4) (2007) 1271–1281 12 Otrocol, D, Rus, IA: Functional differential equations with maxima of ... existence and uniqueness of solutions of a class of fractional differential equations J Math Anal Appl 334 (2007) 1–10 Momani, SM, Ibrahim, RW: On a fractional integral equation of periodic functions

Ngày tải lên: 21/06/2014, 17:20

... the propagation of derivative discontinuities through systems of equations is presented. Following a short resumd of standard techniques for the solution of ordinary differential equations (ODE's), ... solution of systems of delay -differential equations. A novel representation for the differential equation is used to acknowledge structural differences between delay- and ordinary differential systems. ... Solution of Delay -differential Equations by David Richard Wille Department of Mathematics University of Manchester volume I of II A thesis submitted to the University of Manchester for the degree of

Ngày tải lên: 11/10/2014, 04:02

... Solution of Delay -differential Equations by David Richard Wile Department of Mathematics University of Manchester volume II of II A thesis submitted to the University of Manchester for the degree of ... appendix we give a formal proof of the result (1.1.3:14). For any given time let the order of continuity of the component y i be Z i . Our task is thus to obtain a set of lower bounds {c i : > ... closure of E. Heuristically, by an extension of the above arguments, we may think of Ei as defining the set of points whose continuity bounds can affect the continuity bound, c i , of y i .

Ngày tải lên: 11/10/2014, 04:03

... BOUNDARY VALUE PROBLEMS OF DIFFERENTIAL EQUATIONS (5390) The Minh Tran 1. Solution a) Because '' u (x) 1 = , so we have the genaral form of u(x) : ( ) 2 x u ... separate var iableby dividing both sides of (1) by x G(t) dG t 1 1 d sin5x G dt dx G We can not solve by the method of separation of var iables because the presence of a terms like sin5x is forbidden ... sin5x t x We assum that u(x,t) x G t where x is only a function of x and G t is a function of t We will get firstpartial derivetive of u(x,t) w ith respect to t and the fourth partial derivative

Ngày tải lên: 02/11/2014, 13:00