second order linear homogeneous differential equations with variable coefficients

... superlinear growth of the nonlinearity of f (t, p) in p  Inspired by [21,24,25], in this paper, we investigate the following second-order impul-sive nonlinear differential equations with periodic ... pagesdoi:10.1155/2007/41589 Research Article Existence of Solutions for Second-Order Nonlinear Impulsive Differential Equations with Periodic Boundary Value Conditions Chuanzhi Bai and Dandan Yang ... March 2007; Accepted 13 April 2007 Recommended by Kanishka Perera We are concerned with the nonlinear second-order impulsive periodic boundary value problem u (t) = f (t,u(t),u (t)), t ∈[0,T]

Ngày tải lên: 22/06/2014, 19:20

... Trang 1FOR SECOND-ORDER LINEAR FUNCTIONALDIFFERENTIAL EQUATIONS S MUKHIGULASHVILI Received 26 October 2004 and in revised form 7 ... (see [7, Theorem 6, page 88]) for linear ordinary differential equations, and on the other hand describe some properties which belong only to func-tional differential equations In the paper [8], it ... > 0,
: C([0,ω]) → L([0,ω]) is a linear bounded operator, and q ∈ L([0,ω]). 1 Introduction Consider the equation u

(t) =
(u)(t) + q(t) for 0 ≤ t ≤ ω (1.1) with the periodic boundary conditions

Ngày tải lên: 23/06/2014, 00:20

... neutral nonlinear differential equations with delay. Nonlinear Anal 74(12):3926 –3933 (2011) doi:10.1016/j.na.2011.02.029 17 Raffoul, YN: Stability in neutral nonlinear differential equations with ... neutral differential equations with variable delays Proc Am Math Soc 136, 909 –918 (2008) 19 Ardjouni, A, Djoudi, A: Fixed points and stability in linear neutral differential equations with variable ... with Sakthivel and Luo [11,12] investigate the asymptotic stability of the non-linear impulsive stochastic differential equations and the impulsive stochastic partial differential equations with

Ngày tải lên: 20/06/2014, 22:20

... work is properly cited This paper is concerned with some oscillation criteria for the second order neutral delay dynamic equations with mixed nonlinearities of the formrtutΔ qt|xτt| ... pagesdoi:10.1155/2011/513757 Research Article Oscillation Criteria for Second-Order Neutral Delay Dynamic Equations with Mixed Nonlinearities Ethiraju Thandapani,1 Veeraraghavan Piramanantham,2 and ... the second order neutral delay dynamic equations of the form  r t nonnegative rd-continuous functions onT such that rt > 0, and ft, u ≥ qt|u| γ quasilinear neutral delay dynamic equations

Ngày tải lên: 21/06/2014, 05:20

... Differential Equations, vol 232, no 1, pp 277–284, 2007 28 P J Torres, Existence and stability of periodic solutions for second-order semilinear differential equations with a singular nonlinearity,” ... Recommended by Donal O’Regan We present some recent existence results for second-order singular periodic differential equations. A nonlinear alternative principle of Leray-Schauder type, a well-known ... 1.2 It is well known that second order singular differential equations describe many problems in the applied sciences, such as the Brillouin focusing system 1 and nonlinear elasticity 2. Therefore,

Ngày tải lên: 21/06/2014, 20:20

... pagesdoi:10.1155/2008/407352 Research Article Fixed Points and Stability in Neutral Stochastic Differential Equations with Variable Delays Meng Wu, 1 Nan-jing Huang, 1 and Chang-Wen Zhao 2 1 Department of ... stability of a generalized linear neutral stochastic differential equation with variable delays by using the fixed point theory An asymptotic mean square stability theorem with a necessary and sufficient ... deal with the stability for deterministic differential equations, not for stochastic differential equations Very recently, Luo 6 studied the mean square asymptotic stability for a class of linear

Ngày tải lên: 21/06/2014, 23:20

... governedby a class of the second-order nonlinear impulsive differential equation in infinite di-mensional spaces Consider the following second-order nonlinear impulsive differential equations: ¨x(t) = ... 1fference EquationsVolume 2007, Article ID 40160, 17 pages doi:10.1155/2007/40160 Research Article Necessary Conditions of Optimality for Second-Order Nonlinear Impulsive Differential Equations ... semilinear wave equations (see [6, Chapter 6]) Recently, Peng and Xiang [11,12] applied the semigroup theory to establish the existence of optimal controls for a class of second-order nonlinear

Ngày tải lên: 22/06/2014, 19:20

... PSEUDOSPECTRAL METHOD FOR SECOND-ORDER AUTONOMOUS NONLINEAR DIFFERENTIAL EQUATIONS Autonomous nonlinear differential equations constituted a system of ordinary differential equations, which often ... assumed that the second-order autonomous nonlinear differential equations have the types u′′ (x) − u′ (x) = f [u(x)] and u′′ (x) + f [u(x)]u′ (x) + u(x) = on the range [−1, 1] with the boundary ... polynomial, autonomous equations, nonlinear differential equations, Van der Pol oscillator DOI: 10.20537/vm190106 Introduction It is well-known that the autonomous nonlinear differential equations constitute

Ngày tải lên: 24/08/2019, 18:35

... evy-driven McKean-Vlasov SDEs with irregular coefficientsIn this section, we present results concerning the exact solution of the McKean-Vlasov stochastic differential equation with jumps (3.1) First, ... the stochastic differential given by dV(t, X t ) =hTheorem 1.1.6 (The multi-dimensional Itˆo, [62], Theorem 6.4) Let X t be a d-dimensional Itˆo process on t ≥0 with the stochastic differential ... u(t)≤c+Z t 0 v(s)u(s)ds for all 0≤t≤T, then u(t)≤cexpStochastic differential equationsLet (Ω,F, P) be a complete probability space with a filtration {F t } t≥0 satisfying the usual conditions LetWt

Ngày tải lên: 17/09/2025, 16:23

... 2006; Revised 22 May 2006; Accepted 28 May 2006 This paper deals with boundary value problems for second-order differential equations with deviating arguments Some sufficient conditions are formulated ... condition with respect to the last two variables with corresponding functions instead of constants Note that the special case whenf is monotone nonincreasing (with respect to the last two variables) ... Chapter 2] The mono-tone iterative method is useful to obtain approximate solutions of nonlinear differential equations, for details see, for example, [10], see also [1–8,11,12] It has been applied

Ngày tải lên: 22/06/2014, 22:20

... Trang 1HIGHER-ORDER LINEAR DIFFERENTIAL EQUATIONSWITH STRONG SINGULARITIES R P AGARWAL AND I KIGURADZE Received 4 April 2004; Revised ... 11 December 2004; Accepted 14 December 2004 For strongly singular higher-order linear differential equations together with two-pointconjugate and right-focal boundary conditions, we provide easily ... b[) (L2α,β(]a, b[)) is the space of integrable (square integrable) with the weight (t − a) α(b − t) βfunctionsy :]a, b[ → Rwith the norm α(]a, b])) is the space of functions y ∈ Lloc(]a, b[)

Ngày tải lên: 23/06/2014, 00:20

... (greatest) solution This seems to be a peculiar feature of equations with deviated arguments, see [1] for an example with a second-order equation Therefore, we are obliged to distinguish between ... prove some new results on existence of solutions to first-order ordinary differential equations with deviated arguments Delay differential equations are included in our general framework, which even ... (HTML) versions will be made available soon Minimal and maximal solutions to first-order differential equations with state-dependent deviated arguments Boundary Value Problems 2012, 2012:7 doi:10.1186/1687-2770-2012-7

Ngày tải lên: 20/06/2014, 20:20

... problem for second order nonlinearsingular differential equations,” Georgian Mathematical Journal, vol 7, no 1, pp 133–154, 2000.9 Z Yang, “Positive solutions to a system of second-order nonlocal ... nonlinear fourth-order singular p-Laplacian differential equations with integral boundary conditions:  ϕ p xt ft, xt, xt, 0 < t < 1, x0  Trang 20hsds < 1 and nonlinear ... approach,” Journal of the London Mathematical Society Second Series, vol 74, no 3, pp 673–693, 2006. 6 J M Gallardo, “Second-order differential operators with integral boundary conditions and generation

Ngày tải lên: 21/06/2014, 11:20

... for secondorder impulsive differential equations, ”... B S Alghamdi, “Analytic approximation of solutions of the forced Duffing equation with integral boundary conditions, ” Nonlinear ... p-Laplacian fourth-order differential equations with integral boundary conditions. For the case of I k  0,k 1, 2, ,m, g  0,h 0, and p  2, problem 1.6 is related to fourth-order two-points ... doi:10.1155/2011/654871 Research Article Multiple Positive Solutions of Fourth-Order Impulsive Differential Equations with Integral Boundary Conditions and One-Dimensional p-Laplacian Meiqiang Feng

Ngày tải lên: 21/06/2014, 16:20

... self-adjoint differential equations of second order,” Annals of Mathematics, vol 65, pp 197–202, 1957 R Zhuang, “Sturm comparison theorem of solution for second order nonlinear differential equations,” Annals ... comparison theorem of second-order differential equations see Section Remark 3.6 In the discrete case: μ t ≡ This result is the same as Sturm comparison theorem of second-order difference equations see ... of second-order linear equations on time scales We first establish Picone identity on time scales and obtain our main result by using it Also, our result unifies the existing ones of second-order

Ngày tải lên: 21/06/2014, 20:20

... 13 pagesdoi:10.1155/2007/98423 Research Article Oscillation of Higher-Order Neutral-Type Periodic Differential Equations with Distributed Arguments R S Dahiya and A Zafer Received 19 October ... numbers with λ > 0 and μ > 0. Trang 3We may begin with the following comparison theorem.Theorem 2.1 Let δ = 1, α ≥ 0, β < 0, and 1 + α + β > 0 Suppose that (a) equation ( E k μ ) with ... to our assumption (b) combined with the second part ofLemma 3.1, we see that (3.6) cannot have an eventually positive solution of degreen, which is a contradiction with (3.5) Similarly, if the

Ngày tải lên: 22/06/2014, 18:20

... is a homogeneous linear equation that is not r-regular We say that a linear equation or a system of linear equations L is regular if it is r-regular for all r ∈ N Theorem 2 For a linear homogeneous ... integer A linear equation or a system of linear equations L is r-regular if every r-coloring of positive integers admits a monochromatic solution to L Hence Theorem 1 states that a linear homogeneous ... ideas presented in this paper Theorem 1 Let L be a linear homogeneous equation with integer coefficients Assume that L has at least three and not all coefficients of the same sign Then any 2-coloring

Ngày tải lên: 08/08/2014, 12:22

... Trang 1Stability Radius of Linear Dynamic Equations with Constant Coefficients on Time Scales Le Hong Lan!*, Nguyen Chi Liem? | Department of ... dynamic equations with respect to linear dynamic perturbations on time scales A formula for the stability radius is given Keywords and phrases : time scales, exponential function, linear dynamic ... and formula of the stability radius were extended to linear time-invariant differential-algebraic systems [6, 7]; and to linear time-varying differential and difference-algebraic systems [8, 9]

Ngày tải lên: 22/03/2014, 11:20

... “anti-periodic” conditions for differential equations or impulsive differential equations To the best of our knowledge it is the first article to deal with integro-differential equations with “anti-periodic” ... existence of solutions for first-order nonlinear integro-differential equations with boundary value conditions Our methods to prove the existence of solutions involve new differential inequalities and ... works [18,19], we come up with a new approach to ensure the existence of at least one solution for certain family of first-order nonlinear integro-differential equations with periodic boundary value

Ngày tải lên: 21/06/2014, 02:20

... third-order differential equations see 1–20 Various techniques appeared for the investigation of such equations Some of them 1, 19 make use of the methods developed for the second-order equations ... differential equations,” Applied Mathematics and Computation, vol 215, no 12, pp 4392–4399, 2010 17 Y V Rogovchenko and F Tuncay, “Oscillation criteria for second-order nonlinear differential equations with ... differential equations with positive delays,” Archiv der Mathematik, vol 36, no 2, pp 168–178, 1981 16 M Hasanbulli and Y V Rogovchenko, “Oscillation criteria for second order nonlinear neutral

Ngày tải lên: 21/06/2014, 11:20