examples of nonlinear first order differential equations

... (C) To establish the (differential) equations Analysis of the Model (A) To solve equations (B) To find the properties of solutions (C) If it is too difficult to solve the equations, try to approximate ... (C) To establish the (differential) equations Analysis of the Model (A) To solve equations (B) To find the properties of solutions (C) If it is too difficult to solve the equations, try to approximate ... Series and Differential Equations Nguyen Thieu Huy Hanoi University of Science and Technology Nguyen Thieu Huy (HUST) Infinite Series and Diff Eq 1/9 Exact equations 3.1 Definition A differential

Ngày tải lên: 23/04/2020, 08:00

... Trang 1fference EquationsVolume 2007, Article ID 96415, 12 pages doi:10.1155/2007/96415 Research Article Unbounded Perturbations of Nonlinear Second-Order Difference Equations at Resonance ... existence of solutions of nonlinear discrete boundary value problems Δ2u(t −1) +μ1u(t) + g(t,u(t)) = h(t), t ∈ T,u(a) = u(b + 2) =0, whereT:= { a + 1, , b + 1 },h : T → R,μ1is the first eigenvalue of ... generalized zero of ψ2in [a + 1,b + 1]. Then ( 1.6 ) has a solution provided b+1  The analogue ofTheorem 1.4was obtained for two-point BVPs of second-order or-dinary differential equations by Iannacci

Ngày tải lên: 22/06/2014, 19:20

... 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 ... component function ofG maps each boundary point of Ω into Ω itself and then, by breaking up the boundary of Ω into separate pieces, consider the effect of the first component function of G on those ... extend previous ones of Etheridge and Rodriguez [4] who studied the existence of periodic solutions of difference equations under signifi-cantly more restrictive conditions on the nonlinearities 2

Ngày tải lên: 23/06/2014, 00:20

... AccessSolving nonlinear Volterra integro-differential equations of fractional order by using Euler wavelet method Yanxin Wang1*and Li Zhu1,2 * Correspondence: wyxinbj@163.com 1 School of Science, ... and applications of the fractional-order partial differ-ential equations (FPDEs) have become of increasing interest for the researchers to gen-eralize the integer-order differential equations Conventionally ... matrix, the nonlinear fractional integro-differential equations are reduced to a system of algebraic equations which is solved through known numerical algorithms Also, various types of solutions,

Ngày tải lên: 04/12/2022, 16:38

... 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 ... criterion of Lyapunov Am J Math 73, 885–890 (1951) [3] Cheng, SS: Lyapunov inequalities for differential and difference equations Fasc Math 23, 25–41 (1991) [4] He, Z: Existence of two solutions of m-point

Ngày tải lên: 20/06/2014, 21:20

... Article Nonoscillation of First-Order Dynamic Equations with Several Delays Elena Braverman1 and Bas¸ak Karpuz2 1 Department of Mathematics and Statistics, University of Calgary, 2500 University ... areneither delay-differential nor classical difference equations 1 Introduction Oscillation of first-order delay-difference and differential equations has been extensivelystudied in the last two ... and delay-differential equations can be incorporated in the general type of equations called dynamic equations. The objective of this paper is to unify some results obtained in2,3 for the delaydifference

Ngày tải lên: 21/06/2014, 11:20

... Article Existence of Solutions for Nonlinear Fractional Integro-Differential Equations with Three-Point Nonlocal Fractional Boundary Conditions Ahmed Alsaedi and Bashir Ahmad Department of Mathematics, ... work is properly cited We prove the existence and uniqueness of solutions for nonlinear integro-differential equations of fractional order q ∈ 1, 2 with three-point nonlocal fractional boundary ... Conclusions This paper studies the existence and uniqueness of solutions for nonlinear integro-differential equations of fractional order q ∈ 1, 2 with three-point nonlocal fractional boundary

Ngày tải lên: 21/06/2014, 16:20

... optimality of the obtained results 2 Preliminaries This paper is devoted to study the stability, by using the method of lower and upper solutions, of theN-periodic solutions of the following first-order ... 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 ... lie between a lower and an upper solution of suitable operators Our purpose is to ensure the stability of at least one periodic solution of a first-order difference equation We will prove such

Ngày tải lên: 23/06/2014, 00:20

... = 0 Trang 62 NON-AUTONOMOUS EQUATION This p a r a g r a p h is devot ed to study of the differential equation of form (2 1 ) x iN) + a xx (N l) + + a N- ị i + ocNx = eF(x> X, X(N ), ... th e first ap p ro x im a tio n s = 1 an d th e refin em en t o f th e first a p p r o x im a tio n ( 2 1 5 ) X = Yj a s COS <pj + £ Uj(a, 0) , 5=1 where av <PS are the solution of equation ... lu t io n o f e q u a tio n (1.1) in th e first a p p r o x im a tio n : (1.17) X = £ a , COS (i2sf + >J/S) , 5=1 an d r e fin e m e n t o f th e first ap p roxim ation : (1.18) X COS (

Ngày tải lên: 08/04/2015, 15:36

... at some of the boundary value problems for the nonlinear fourth-order differential equations Firstly, consider the problem of elastic beams as described by the nonlinear fourth-order differential ... problems for differential equations Among the differential equations, the nonlinear fourth-order differential equation has been of great interest recently as it is the mathematical model of many ... possible to classify the fourth-order differential equations into two forms: fully order differential equations and non-fully fourth-order ones A fourth-fourth-order differential equation whose right-hand

Ngày tải lên: 01/04/2021, 19:17

... Trang 1R E S E A R C H Open AccessExistence and uniqueness of solutions for multi-term nonlinear fractional integro-differential equations Dumitru Baleanu1,2,3*, Sayyedeh Zahra Nazemi4and Shahram ... list of author information is available at the end of the article Abstract In this manuscript, by using the fixed point theorems, the existence and the uniqueness of solutions for multi-term nonlinear ... differential equation 1 Introduction The study of fractional differential equations ranges from the theoretical aspects of ex-istence and uniqueness of solutions to the analytic and numerical methods

Ngày tải lên: 02/11/2022, 10:38

... stability of the first-order matrix difference equations * Correspondence: smjung@hongik.ac.kr Mathematics Section, College of Science and Technology, Hongik University, Sejong, 339-701, Republic of ... which the value of vector of variables at one point is dependent on the values of preceding (suc-ceeding) points In this paper, we prove the Hyers-Ulam stability of the first-order linear homogeneous ... (or nonlinear) recurrences Especially in , the Hyers-Ulam stability of the first-order matrix difference equations has been proved in [] in a general setting The substantial difference of this

Ngày tải lên: 02/11/2022, 11:35

... in study of stability of differential equations By applying the generalized Halanay inequality, the stability results of nonlinear neutral functional differential equations NFDEs and nonlinear ... Halanay Inequality for Stability of Nonlinear Neutral Functional Differential Equations Wansheng Wang School of Mathematics and Computational Science, Changsha University of Science and Technology, ... differential equations NFDEs and a class of nonlinear neutral delay integrodifferential equationsNDIDEs 2 Generalized Halanay Inequality In this section, we first give a generalization ofLemma

Ngày tải lên: 21/06/2014, 07:20

... the existence of one-sign solutions of the nonlinear problem x ft, x, t ∈ 0, T, x 0  xT, x0  xT. 1.18 The proofs of the main results are based on the properties of G and the ... result concerning the global structure of the set of positive solutionsof parameterized nonlinear operator equations, which is essentially a consequence of Dancer 12, Theorem 2 Suppose thatE ... pagesdoi:10.1155/2010/626054 Research Article Existence of Positive Solutions of Nonlinear Second-Order Periodic Boundary Value Problems Ruyun Ma, Chenghua Gao, and Ruipeng Chen Department of Mathematics, Northwest Normal

Ngày tải lên: 21/06/2014, 11:20

... 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, ... 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 ... solutions of singular third-order three-point boundary value problem,” Journal of Mathematical Analysis and Applications, vol 306, no 2, pp 589–603, 2005. 14 B Yang, “Positive solutions of a third-order

Ngày tải lên: 21/06/2014, 11:20

... are a number of definitions for the stability of stochastic systems Acommon choice of definition amongst numerical analysts investigating stochastic differ-ential equations is that of mean square ... supports of a bridge, possibly changing thelong-term integrity of the structure) It is a natural extension of the deterministic workcarried out by ourselves and others to consider the stability of ... theory of stochastic differential equations type of (1.1) was studied by Gikhman and rokhod [10] Sko-The selected test equation (1.1) arises from the deterministic linear test equation ofBrunner

Ngày tải lên: 22/06/2014, 22:20

... Fourth-order nonlinear differential equations have many applications such as balancing condition of an elastic beam which may be described by nonlinear fourth-order ordinary differential equations ... pagesdoi: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; ... methods of our proof, we can show that SBVP (2.47) has the similar conclusions of Theorems2.3–2.5 3 Continuous case We consider boundary value problems of system for nonlinear fourth-order ordinary

Ngày tải lên: 22/06/2014, 22:20

... therein However, compared to second-order difference equations of type (1.4;δ), the study of higher-order equations, and in particular third-order equations of type (1.1;δ) has received considerably ... second order nonlinear difference equations, J Math Anal Appl 204 (1996), no 3, 813–829 X Zhou and J Yan, Oscillatory and asymptotic properties of higher order nonlinear difference equations, Nonlinear ... Difference Equations 2005:3 (2005) 345–367 DOI: 10.1155/ADE.2005.345 346 On the oscillation of certain third-order difference equations The oscillatory behavior of second-order half-linear difference equations

Ngày tải lên: 23/06/2014, 00:20

... (Method of Limiting Equations) Gordon and Breach: Amsterdam, 1996 11 Linh NM, Phat VN Exponential stability of nonlinear time-varying differential equations and applications Electronic Journal of Differential ... stability of nonlinear time-varying differential equations and partial averaging Mathematics of Control, Signals, and Systems 2002; 15:42–70 16 Phat VN On the stability of time-varying differential equations ... The remainder of the proof is similar to that of the proof of Theorem 2.2 Suppose all hypotheses of Corollary 2.4 hold Thus, (10) is exponentially stable Consider a perturbed system of the form

Ngày tải lên: 16/12/2017, 10:05

... defined Also morphic differential. mero-Sometimes, analytic differentials are call-ed Abelian differentials of the first kind, meromorphic differentials with only larities of order≥ 2 are called ... q j, where each p i is a zero of f a of order a i and each q j is a pole of f a of order b j canonical divisor class The module n (X) of n-dimensional regular differential forms on an n-dimensional, ... Theorem. calculus of variations The study of certain problems of minimization of integrals Typi-cal is the fundamental problem of the Typi-calculus of variations: Given a function of three vari-ables,

Ngày tải lên: 19/03/2018, 15:57