solving first order linear differential equations with constant coefficients

... element to the element Φ in S according to multiplication ◦ in group Ᏻ Linear functional equations of the kth order with constant coefficients Let a j ∈ R, j = 0,1,2, ,k Then the equation ak f ◦ ... (x) + a0 f ◦ Φ0 (x) = (2.1) in S is called a linear homogeneous functional equation of kth order with constant coefficients The coefficients are the constants a j , j = 0,1,2, ,k It is assumed that ... While constant functions are automorphic with respect to any Φ, there are examples of nonconstant automorphic functions One such is p(x) = sin(π(x − n)) on A remark on linear functional equations...

Ngày tải lên: 22/06/2014, 22:20

... value problems for systems of higherorder ordinary differential equations with singularities, Georgian Mathematical Journal (1994), no 1, 31–45 32 Linear BVPs with strong singularities [13] V E ... differential equations of higher order, Georgian Mathematical Journal (2001), no 4, 791–814 [11] I T Kiguradze and B L Shekhter, Singular boundary value problems for second -order ordinary differential equations, ... Fredholm property since the constant r does not depend on q 28 Linear BVPs with strong singularities Proof of Corollary 1.4 By conditions (1.23), there exist positive constants m), satisfying inequalities...

Ngày tải lên: 23/06/2014, 00:20

Ngày tải lên: 22/03/2014, 11:20

... p-Laplacian fourth -order differential equations with integral boundary conditions 0, k 1, 2, , m, g 0, h 0, and p 2, problem 1.6 is For the case of Ik related to fourth -order two-points boundary ... paper are as follows Firstly, comparing with 39–43 , we discuss the impulsive boundary value problem with integral boundary conditions, that is, problem 1.6 includes fourth -order two-, three-, ... second order impulsive differential equations with advanced arguments,” Applied Mathematics and Computation, vol 197, no 1, pp 179–189, 2008 17 T Jankowski, “Positive solutions to second order...

Ngày tải lên: 21/06/2014, 16:20

... motivation of our investigation goes back to [10] dealing with the linear system of differential equations with constant coefficients and constant delay One of the systems considered has the form ... higher -order monotone difference equations, Advances in Difference Equations 2005 (2005), no 1, 41–55 [12] M Migda, A Musielak, and E Schmeidel, On a class of fourth -order nonlinear difference equations, ... Difference Equations 2004 (2004), no 1, 23–36 [13] Ch G Philos and I K Purnaras, An asymptotic result for some delay difference equations with continuous variable, Advances in Difference Equations...

Ngày tải lên: 22/06/2014, 22:20

... solutions First- order differential equations with state-dependent deviated arguments have received a lot of attention in the last years We can cite the recent articles [2–7] which deal with existence ... (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...

Ngày tải lên: 20/06/2014, 20:20

... equations with piecewise constant arguments,” Acta Mathematica Sinica, vol 18, no 2, pp 263–276, 2002 H.-X Li, “Almost periodic solutions of second -order neutral delay-differential equations with ... differential equations with piecewise constant delays,” Journal of Mathematical Analysis and Applications, vol 99, no 1, pp 265–297, 1984 S M Shah and J Wiener, “Advanced differential equations with piecewise ... R Yuan, “On the spectrum of almost periodic solution of second -order differential equations with piecewise constant argument,” Nonlinear Analysis: Theory, Methods & Applications, vol 59, no 8,...

Ngày tải lên: 21/06/2014, 20:20

... Maple Linear first -order differential equations Applications of linear first -order differential equations Mixing problems Exponential growth and decay Newton’s law of Cooling Nonlinear first -order differential ... subjects of differential equations and linear algebra, the presentation begins with first -order differential equations, followed by second- and higher order linear differential equations Following ... general solutions to systems of linear differential equations or higher order linear differential equations Over the past decade or two, first -order differential equations have become a standard...

Ngày tải lên: 11/06/2014, 07:16

... W: On some nonlinear ordinary differential equations with advanced arguments Nonlinear Anal 2003, 53:495-505 Yan JR: Oscillation of first- order impulsive differential equations with advanced ... problem for non -linear differential equations of fractional order Nonlinear Anal 2011, 74:792-804 Zhang L, Wang G: Existence of solutions for nonlinear fractional differential equations with impulses ... problem for second order differential equations with an advanced argument Nonlinear Anal 2006, 65:2013-2023 Jankowski T: Positive solutions for fourth -order differential equations with deviating...

Ngày tải lên: 21/06/2014, 03:20

... equation” 2.1 Next we consider a nonlinear first -order difference equation 6 Advances in Difference Equations 2.2 The Bound Estimate of a Solution to a Nonlinear First- Order Difference Equation Lemma ... second -order linear difference equations, ” Journal of Computational and Applied Mathematics, vol 41, no 1-2, pp 65–94, 1992 R Wong and H Li, “Asymptotic expansions for second -order linear difference equations ... to second order linear difference equations in the first case For the second case, we leave it to the second part of this paper: Error Bound for Asymptotic Solutions of Second -order Linear Difference...

Ngày tải lên: 21/06/2014, 11:20

... problem for second order nonlinear singular differential equations, ” Georgian Mathematical Journal, vol 7, no 1, pp 133–154, 2000 Z Yang, “Positive solutions to a system of second -order nonlocal boundary ... p-Laplacian fourth -order differential equations with integral boundary conditions,” Journal of Computational and Applied Mathematics, vol 222, no 2, pp 561–573, 2008 14 C Corduneanu, Integral Equations ... integral condition holds: 0< s − s f s, − s ds < ∞ 4.7 Consider the fourth -order singular p-Laplacian differential equations with integral conditions: f t, x t , x t , ϕp x t x x 0, < t < 1, g s x...

Ngày tải lên: 21/06/2014, 11:20

... 2007 Advances in Difference Equations 14 J Li and J Shen, “Positive solutions for first order difference equations with impulses,” International Journal of Difference Equations, vol 1, no 2, pp 225–239, ... differential equations with impulses,” Mathematica Applicata, vol 17, no 3, pp 456–463, 2004 13 J Li, J J Nieto, and J Shen, “Impulsive periodic boundary value problems of first -order differential equations, ” ... equations, ” Journal of Computational and Applied Mathematics, vol 138, no 2, pp 205–217, 2002 11 Z He and X Zhang, “Monotone iterative technique for first order impulsive difference equations with...

Ngày tải lên: 21/06/2014, 20:20

... in Difference Equations One of the methods used to study 1.1 is transforming the second -order delay differential equation to a first -order differential or integrodifferential equations with delay A ... comparison with the method used in is that a second order delay equation is reduced to one first -order integrodifferential delay equation while in a second -order equation is reduced to a system of a nonlinear ... N Minorsky, Nonlinear Oscillations, D Van Nostrand, Princeton, NJ, USA, 1962 L Berezansky and E Braverman, “Nonoscillation of a second order linear delay differential equation with a middle term,”...

Ngày tải lên: 21/06/2014, 20:20

... neutral differential equations, ” Annals of Differential Equations, vol 19, no 1, pp 65–70, 2003 [20] S H Saker, “Oscillation of higher order neutral delay differential equations with variable coefficients,” ... functional-differential equations, ” Computers & Mathematics with Applications, vol 38, no 11-12, pp 1–11, 1999 [4] D D Ba˘nov and D P Mishev, Oscillation Theory for Neutral Differential Equations with Delay, ... differential equations with deviating arguments,” ı Hiroshima Mathematical Journal, vol 10, no 3, pp 495–516, 1980 [22] S Tanaka, “Oscillation of solutions of even order neutral differential equations, ”...

Ngày tải lên: 22/06/2014, 18:20

... allow 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 impulsive nonlinear differential equations with periodic ... ordinary differential equations, ” Nonlinear Analysis, vol 51, no 7, pp 1223–1232, 2002 [24] C Bai, “Existence of solutions for second order nonlinear functional differential equations with periodic boundary ... population,” Nonlinear Analysis: Real World Applications, vol 4, no 4, pp 639–651, 2003 [16] R P Agarwal and D O’Regan, “Multiple nonnegative solutions for second order impulsive differential equations, ”...

Ngày tải lên: 22/06/2014, 19:20

... the second -order impulsive functional differential equations, Computers & Mathematics with Applications 50 (2005), no 34, 491–507 [2] T Jankowski, Advanced differential equations with nonlinear boundary ... differential equations with nonlinear boundary conditions, Boundary Value [3] Problems 2005 (2005), no 2, 201–214 , Solvability of three point boundary value problems for second order differential equations ... functional differential equations, Nonlinear Analysis 50 (2002), no 7, 885–898 [8] D Jiang, P Weng, and X Li, Periodic boundary value problems for second order differential equations with delay and monotone...

Ngày tải lên: 22/06/2014, 22:20

Ngày tải lên: 11/03/2015, 07:57

... Functional differential equations with state-dependent delays: theory and applications, in: A Canada, P Drabek, A Fonda (Eds.), Handbook of Differential Equations: Ordinary Differential Equations, ... note on partial functional differential equations with state-dependent delay, Nonlinear Anal Real World Appl (4) (2006) 510–519 [25] A.V Rezounenko, Differential equations with discrete state-dependent ... Inertial manifolds for retarded semilinear parabolic equations, Nonlinear Anal 34 (1998) 907–925 [8] J Wu, Theory and Applications of Partial Functional Differential Equations, Springer-Verlag, New...

Ngày tải lên: 29/10/2015, 14:19

... 0} with intensity λ > is a piecewise constant process with stationary independent increments with initial value N0 = such that Nt − Ns is Poisson distributed with intensity λt−s , that is, with ... achieves an order γ of strong convergence, then it also achieves at least an order β = γ of weak convergence We emphasize that the weak order obtained above is usually not sharp and, thus, the order ... research monograph may be of assistance 1 Stochastic Differential Equations with Jumps Stochastic differential equations (SDEs) with jumps provide the most flexible, numerically accessible, mathematical...

Ngày tải lên: 19/02/2014, 22:20

Ngày tải lên: 14/03/2014, 13:20