system of nonlinear differential equations examples

... 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 ... In 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+ ... 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

Ngày tải lên: 21/06/2014, 03:20

... solve various kinds of nonlinear equations The new homotopy perturbation method NHPM was applied to linear and nonlinear ODEs 17 In this paper, we construct the solution of system of fractional-order ... 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 ... 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

Ngày tải lên: 21/06/2014, 05:20

... N . The proof of Lemma 3.1 is given for completeness in the appendix of this article. Lemma 3.2 is an extension of [17, Lemma 1], so the proof is omitted here for briefness. Proof of Theorem ... equilibrium solu- tions to system (1.5)in R N are corresponding to the entire positive solutions of a system in the form of (1.1). Some existence results of elliptic system Δu + F 1 (x, u,v) = ... existence of positive entire solutions cannot be derived from those in the literature. The aim of this article is to develop the theory of existence of positive solutions for nonlinear elliptic systems.

Ngày tải lên: 22/06/2014, 22:20

... non-linear system of wave equations Nonlinear Analysis 2007; 67:3136–3151 13 Santos ML Decay rates for solutions of a system of wave equations with memory Electronic Journal of Differential Equations ... a system of nonlinear equations with nonlinear boundary conditions First, on the basis of the Faedo–Galerkin method and standard arguments of density corresponding to the regularity of initial ... asymptotic behavior of solutions were obtained In [12], Miao and Zhu proved the existence and regularity of global smooth solutions of a Cauchy problem for the nonlinear system of wave equations with

Ngày tải lên: 18/12/2017, 08:41

... dynamics of a network is represented by a system of nonlinear differential equations with or without delay.In the past two decades, the study involving qualitative behavior of nonlinear systems ... Stability of nonlinear time-delay systems in BAM-Cohen-Grossberg neural networksConsider the following system of differential equations with delays x 0 i (t) = αi(xi(t)) hSystem (1) describes a type of ... addition, because of the infinite-dimensional nature of the phase space, the qualitative study of time-delay systems becomes much more complicated than that of ordinary differential equation systems A

Ngày tải lên: 31/07/2024, 16:30

... dynamics of a network is represented by a system ofnonlinear differential equations with or without delay In the past two decades, the study in-volving qualitative behavior of nonlinear systems ... solutions and stability of nonlinear differential equations withdelays B Research aims The thesis focuses on problems of stability of several classes of nonlinear positive ential systems with delay ... presentation of the results in next chapters 1.1 Nonnegative matrix and M-matrix 1.2 System of delayed differential equations and Lyapunov stability 1.3 Positive system and stablity of nonlinear

Ngày tải lên: 31/07/2024, 17:01

... differential equations of third order,” ¸ Nonlinear Dynamics and Systems Theory, vol 7, no 4, pp 419–430, 2007 24 C Tunc, “On the nonoscillation of solutions of nonhomogeneous third order differential equations,” ... boundedness of the solutions of third-order nonlinear differential ¸ equations,” Kuwait Journal of Science & Engineering, vol 32, no 1, pp 39–48, 2005 28 E Tunc, “On the convergence of solutions of certain ... “Oscillatory properties of solutions of certain nonlinear third order s differential equations,” Nonlinear Studies, vol 7, no 1, pp 43–50, 2000 P Hartman, Ordinary Differential Equations, Classics

Ngày tải lên: 22/06/2014, 02:20

... 16 Integration of Ordinary Differential Equations Note that for compatibility with bsstep the arrays y and d2y are of length 2n for a system of n second-order equations The values of y are stored ... vol 27, pp 505–535 16.6 Stiff Sets of Equations As soon as one deals with more than one first-order differential equation, the possibility of a stiff set of equations arises Stiffness occurs in ... classes of higher-order methods for stiff systems: • Generalizations of the Runge-Kutta method, of which the most useful are the Rosenbrock methods The first practical implementation of these

Ngày tải lên: 24/12/2013, 12:16

... 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

... 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

... 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

... nonnegative numbers System (1) was mentioned in [1] as one of three systems of Open Problem 3, which asked for a description of the global dynamics of some rational systems of difference equations In ... Difference Equations 2011, 2011:29 http://www.advancesindifferenceequations.com/content/2011/1/29 RESEARCH Open Access Dynamics of a two-dimensional system of rational difference equations of Leslie–Gower ... for global dynamics of the System (1) is determining the basins of attraction of different equilibrium points The difficulty in analyzing the behavior of all solutions of the System (1) lies in

Ngày tải lên: 21/06/2014, 00:20

... that I u ≥ α, that is, assumption ii of Lemma 2.1 holds The proof of Theorem 1.2 is completed 14 Advances in Difference Equations Proof of Theorem 1.4 In view of Lemma 2.4, I ∈ C1 E, R We first ... function u∗ is a desired classical solution of 1.1 Since d > 0, u∗ is a nontrivial homoclinic solution The proof is complete Proof of Theorem 1.2 In the proof of Theorem 1.1, the condition that F2 ... Hamiltonian systems and their importance in the study of the behavior of dynamical systems have been already recognized from Poincar´ ; homoclinic orbits play an important role in analyzing the chaos of

Ngày tải lên: 21/06/2014, 11:20

... 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

... Hamilton-Jacobi equations to nonlinear parabolic equations, then by using Perron’s method to study the existence and uniqueness of time almost periodic viscosity solutions of nonlinear parabolic equations ... Problems the proof of existence of viscosity solutions of first-order Hamilton-Jacobi equations, Crandall et al. had applications of Perron’s Method to second-order partial differential equations in ... almost periodic viscosity solutions of first-order Hamilton-Jacobi equations. Nunziante considered the existence and uniqueness of viscosity solutions of parabolic equations with discontinuous time

Ngày tải lên: 21/06/2014, 20:20

... for solving a system of nonlinear inclusions in Banach spaces. We prove some new existence results of solutions for the system of nonlinear inclusions and discuss the convergence of the sequences ... solving the system of nonlinear inclusions problem (1.3)inBanachspaces. We prove the existence of solution for the system of nonlinear inclusions problem (1.3) and the convergence of the sequences ... cases of problem (1.3). 4. Existence and convergence In this section, we will prove the existence of solutions for the system of nonlinear inclu- sions problem (1.3) and the convergence of sequences

Ngày tải lên: 22/06/2014, 22:20

... doi:10.1155/2007/76493 Research Article Positive Solutions of Boundary Value Problems for System of Nonlinear Fourth-Order Differential Equations Shengli Xie and Jiang Zhu Received 23 March 2006; ... similar methods of our proof, we can show that SBVP (2.47) has the similar conclusions of Theorems 2.3–2.5. 3. Continuous case We consider boundary value problems of system for nonlinear fourth-order ... Section 2, we prove the existence of the positive solutions and the multiple positive solutions for systems of nonlinear fourth- order boundary value problems with nonlinear singular terms f i (t,u)

Ngày tải lên: 22/06/2014, 22:20

... 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 ... 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.

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