solution of nonlinear algebraic equations pdf

... have been written as part of a Ph.D course on the numerical solution of Differential Algebraic Equations The course was held at IMM in the fall of 1998 The authors of the different chapters have ... IMM DEPARTMENT OF MATHEMATICAL MODELLING Technical University of Denmark DK-2800 Lyngby – Denmark May 6, 1999 CBE Numerical Solution of Differential Algebraic Equations Editors: Claus ... Computation of Impasse Points of Quasi-Linear Differential-Algebraic Equations Math Comp., 62(205):133–154, January 1994 [PR94b] W.C Rheinboldt P.J Rabier On the Computation of Impasse Points of Quasi-Linear

Ngày tải lên: 21/12/2016, 10:52

... Nonnegative Solution of Nonlinear Impulsive Differential Equations on Infinite Interval 1 Department of Mathematics and Physics, North China Electric Power University, Beijing 102206, China 2 School of ... investigate the existence of minimal nonnegative solution for a class of second-order nonlinear impulsive differential equations on an infinite interval with an infinite number of impulsive times Consider ... economics The theory of impulsive differential equations has become an important area of investigation in the recent years and is much richer than the corresponding theory of differential equations For

Ngày tải lên: 21/06/2014, 11:20

... Bounds for the Solution of the Algebraic Riccati Equations Komaroff 1994 in 16 obtained the following Let K be the positive semidefinite solution of the ARE1.4 Then the trace of K has the ... product of two general matrices The new trace bounds improve the previous results Then, we present some trace bounds for the solution of the algebraic Riccati equations, which improve some of the ... the solution of the AREsee 6 16 Moreover, in terms of 2,6, we know that an interpretation of trK is that trK/n is the average value of the optimal cost J∗as x0varies over the surface of

Ngày tải lên: 22/06/2014, 03:20

... the 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 ... 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 ... Stabilization of solutions of a degenerate nonlinear diffusion problem, Nonlinear Analysis 6 (1982), no. 10, 1001–1022. [3] A. Callegari and A. Nachman, Some singular, nonlinear differential equations

Ngày tải lên: 22/06/2014, 22:20

... 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 ... 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 ... papers 1–3, 11–14 , the authors studied the existence of periodic solutions, subharmonic solutions, and homoclinic solutions of some special forms of 1.1 by using the critical point theory These papers

Ngày tải lên: 21/06/2014, 11:20

... monotone positive solution of the BVP 1.3 Theorem 3.2 If H1f∞< 1 < H2f0, then the BVP1.3 has at least one monotone positive solution Proof The proof is similar to that ofTheorem 3.1and ... existence and nonexistence of monotone positive solution to the above problem 1 Introduction Third-order differential equations arise in a variety of different areas of applied mathematics and ... Monotone Positive Solution of Nonlinear Third-Order BVP with Integral Boundary Conditions Jian-Ping Sun and Hai-Bao Li Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou,

Ngày tải lên: 21/06/2014, 11:20

... 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 ... Trang 2the proof of existence of viscosity solutions of first-order Hamilton-Jacobi equations, Crandallet al had applications of Perron’s Method to second-order partial differential equations in ... and almost periodic viscosity solutions of first-order Hamilton-Jacobi equations Nunziante considered the existence and uniqueness of viscosity solutions of parabolic equations with discontinuous

Ngày tải lên: 21/06/2014, 20:20

... case (ii) of ( 4.2 ), (vi) in particular, g satisfies ( A ) or ( T ), and f and g are solutions of ( A f g ) in the case (ii) of ( 4.2 ). Proof Take the case (i) of (a) Assume that (i) of (4.1) ... solutions of ( T f g ), (ii) f satisfies ( S ) under 2-divisible and one of the cases f (0) = 0, f (x) = f ( − x), (iii) in particular, g satisfies ( A ) or ( T ), and f and g are solutions of ... and g are solutions of g(x + y) − g(x − y) = 2f (x)g(y); (b) if g fails to be bounded, then (i) f and g are solutions of ( T f g ), (ii) f satisfies ( S ) under 2-divisible and one of the cases

Ngày tải lên: 21/06/2014, 22:20

... the proof see Lemma A.1 in the appendix of this paper) Therefore, (1 ) has unique nontrivial solution in the set M Let u be the solution from Theorem 3.1, that is, u is a solution to ... subset of the space Ꮿ((0,1]L2 ([0, ∞))) (for the proof see Lemma A.1 in the appendix of this paper) Therefore (1 ) has unique nontrivial solution in the set M Let u be the solution ... t →0 L2 ([0,∞)) = ∞ (3.62) Svetlin Georgiev Georgiev 23 4 Proof of Theorem 1.2 4.1 Local existence of nontrivial solutions of nonhomogeneous Cauchy problem (1), (2) In this section we

Ngày tải lên: 22/06/2014, 19:20

... The Numerical 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 ... 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), ... consider the development of numerical software for the solution of such problems. Our discussion opens with a brief introduction to the theory of delay-differential equations. Attention is paid

Ngày tải lên: 11/10/2014, 04:02

... The Numerical 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 ... 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

... problems.The nature of differential-algebraic equations (DAEs) is much more complicated Exceptfor the less interesting case of index-0 DAEs, all fundamental solution matrices of regularDAEs are ... each fundamental solution matrix of (53) represents at the same time a damental solution of the DAE (54) Therefore, having in mind wanted appropriate relations fun-of fundamental solution matrices, ... justified as adjoint of (5), see also [26] Incontrast, here we do not make use of functional-analytic arguments, but we try to argue fromappropriate aspects of the theory of differential equations For

Ngày tải lên: 16/12/2017, 06:14

... Differential-algebraic equations; Adjoint pairs of differential-algebraic equations; Self-adjoint boundary value problems 1 Introduction Recently, differential-algebraic equations (DAEs) of the form ... to equations from which they are derived On the other hand, (14) and (15) form an adjoint pair of ODEs Trivially, x ∈ C1 D (x∗∈ C1 A∗) is a solution of (1) ((2)) if and only if Dx (A∗x∗) is a solution ... Q1D− c
D  Q1x A consequence of (23) is that the projections of the right side also vanish We obtain that in fact, (23) is equivalent to a system of algebraic equations: The hidden constraint

Ngày tải lên: 16/12/2017, 15:41

... solutions for a 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 ... 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 ... existence of global solutions and the asymptotic behavior of the energy related to a degenerate system of wave equations with boundary conditions of memory type By the construction of a suitable

Ngày tải lên: 18/12/2017, 08:41

... analysis of the positivity of solutions and the establishment of the exponential stability conditions for the positive equilibrium of such systems.This study addresses the positivity of solutions ... investigates the positivity of solutions and exponential stability of positive equilibrium in nonlinear differential equations with delays, focusing on various types of neural networks The main ... Typically, 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

Ngày tải lên: 31/07/2024, 16:30

... Trang 1MINISTRY OF EDUCATION AND TRAININGHANOI NATIONAL UNIVERSITY OF EDUCATION ——————–o0o——————— LE THI HONG DUNG STABILITY OF POSITIVE SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS WITH DELAYS ... positive 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 ... is concerned with the positivity of solutions and exponential stability ofpositive equilibrium of nonlinear differential equations with delays in various types of neuralnetworks Main contribution

Ngày tải lên: 31/07/2024, 17:01

... of Second-Order Mixed-Nonlinear Delay Dynamic Equations M ¨ Unal1 and A Zafer2 1 Department of Software Engineering, Bahc¸es¸ehir University, Bes¸iktas¸, 34538 Istanbul, Turkey 2 Department of ... ≡ 0 is oscillatory. Proof We will just highlight the proof since it is the same as the proof ofTheorem 2.6 We should remark here that taking et ≡ 0 and η0 0 in proof ofTheorem 2.6, we arrive ... Some of these interval oscillation criteria were recently extended to second-order dynamic equations in 6 10 on oscillatory and nonoscillatory behavior of the second order nonlinear dynamic equations

Ngày tải lên: 21/06/2014, 18:20

... regularity results for weak solutions of (1.1) do not hold without logarith-mic condition on modulus of continuity Variants of this condition have been expedient tools in the study of maximal functions, ... representative Thus it is possible to study pointwise behavior of supersolutions Our main result states that the singular set of a supersolution is of zero capacity For the capacity theory in variable ... possibly unbounded supersolutions of (1.1) and hence the previously obtained estimates are not immediately available for us The main nov-elty of our approach is that instead of the boundedness we

Ngày tải lên: 22/06/2014, 22:20

... 1DIFFERENCE EQUATIONSJES ´US RODRIGUEZ AND DEBRA LYNN ETHERIDGE Received 6 August 2004 We establish conditions for the existence of periodic solutions of nonlinear, second-order difference equations of ... of π. 1 Introduction In this paper, we study the existence of periodic solutions of nonlinear, second-order, discrete time equations of the form y(t + 2) + by(t + 1) + cy(t) = f
y(t), t =0, 1, ... periodic solutions of every odd period larger than one The results presented in this paper extend previous ones of Etheridge and Rodriguez [4] who studied the existence of periodic solutions of difference

Ngày tải lên: 23/06/2014, 00:20

... consisting of a system of ordinary differential equations (ODEs) and a system of algebraic equations so that we can use methods and results of the theory of ODEs Many results on stability properties of ... the theory of ODE we show that each solution of (3.1) is a solution of a linear equation of the form Trang 8A(t)x  + B(t)x + F (t)x = 0. (3.3)Theorem 3.1 Any nontrivial solution x0(t) of the perturbed ... initial value problem of (3.1) has a unique solution” (ii) Different solutions of (3.1) lead to different coefficient matrices of (3.3), hence they are solutions of different linear DAEs of type (3.3) Theorem

Ngày tải lên: 06/08/2014, 05:20