GENERAL FIRST ORDER LINEAR DIFFERENCE EQUATIONS

Outline of course: Introduction: definitions examples First order PDEs: linear & semilinear characteristics quasilinear nonlinear system of equations Second order linear PDEs: classifica[r]

10 M. Cecchi, Z. Doˇsl´a, M. Marini, and I. Vrkoˇc, “Asymptotic properties for half-linear di ff erence
equations,” Mathematica Bohemica, vol. 131, no. 4, pp. 347–363, 2006.
11 O. Doˇsl ´y and ´ A. Elbert, “Integral characterization of the principal solution of half-linear[r]

Program on Dynamical Systems and Ordinary Di ff erential Equations held at the Nankai Insti- tute of Mathematics (Tianjin, 1990/1991) (S. T. Liao, Y. Q. Ye, and T. R. Ding, eds.), Nankai Ser. Pure Appl. Math. Theoret. Phys., vol. 4, World Scientific, New Jersey, 1993, pp. 66–72.
[7] , An Int[r]

C j = C j ( q k 1 , . . . , q k n ) , C j = C j ( q k 1 , . . . , q k i − 1 , q k i +1
, q k i +1 , . . . , q k n ) for all j.
A more detailed exposition of the q -difference case will appear elsewhere. Similarly to the classical case, see [JM], discrete Painlev´e equations of [JS], [Sak][r]

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Stability criteria for linear Hamiltonian dynamic systems on time scales
Advances in Difference Equations 2011, 20[r]

SYSTEMS OF LINEAR EQUATION ---Basis variable: Free variable: General Solution: Find the general solution of the linear system TRANG 17 I.. SYSTEMS OF LINEAR EQUATIONS ---Find the general[r]

n = 1, 2,... } consisting of functions which are solutions of a boundary-value problem for certain second order linear ordinary differential equations.
Let p ( x ), q ( x ), w ( x ) be real continuous functions on the interval [ a , b ]. Let p ( x ) be continuous and p[r]

equations, Journal of Biomathematics 18 (2003), no. 3, 295–298 (Chinese).
[3] Q. Meng and J. R. Yan, Su fficient conditions for the oscillation of non-autonomous difference equa-
tions, Acta Mathematicae Applicatae Sinica 18 (2002), no. 2, 325–332.
[4] Q. G. Tang and Y. B. Deng, Oscillatio[r]

We give su ffi cient conditions so that all solutions of di ff erential equations r t y t q t k y t
p t y α g t f t , t ≥ t 0 , and r t y t q t k y t p t h y g t f t , t ≥ t 0 , are nonoscillatory. Depending on these criteria, some results which exist in[r]

[r]

Then ( 1.14 ) is oscillatory if p∗ > 1 / 4, and nonoscillatory if p ∗ < 1 / 4. The equation can be either oscillatory or nonoscillatory if either p∗ or p ∗ = 1 / 4.
So the following question arises: can one extend the Hille-Kneser theorem to the half- linear dynamic equations L[r]

As a cone in R k+1 , each C µ induces a partial order ≤ µ on R k+1 by x ≤ µ y if and only if
y − x ∈ C µ . We write x < µ y if x ≤ µ y and x = y . The strong ordering µ is defined by
x µ y if and only if y − x ∈ int C µ . The ordering ≤ µ is called the discrete exponential ordering[r]

phân c ấp 2.
ABSTRACT
This paper presents a new approach to solve differential equations of the second order constant factor with initial conditions (Cauchy problem) with THE help of program written with the Maple software. This program is then applied to some linear equ[r]

[9] O. Doˇsl´y and S. Pe˜ na, A linearization method in oscillation theory of half-linear second-order dif-
ferential equations, Journal of Inequalities and Applications 2005 (2005), no. 5, 535–545.
[10] O. Doˇsl´y and P. ˇReh´ak, Half-Linear Di ff erential Equation[r]

To solve this integral equation, direct and inverse Laplace transforms are used.. LINEAR EQUATIONS OF THE FIRST KIND WITH CONSTANT LIMITS OF INTEGRATION 1.[r]

z = x/a , y ( x ) = w ( z ). And we obtain
w ( z + 1) – f ( az ) w ( z ) = 0.
17.2.1-2. Linear difference equations with rational and exponential functions.
Below we give some particular solutions of some homogeneous linear difference equations with ra[r]

The aim of this work is to present numerical treatments to a complex order fractional nonlinear onedimensional problem of Burgers’ equations. A new parameter rt is presented in order to be consistent with the physical model problem. This parameter characterizes the existence of fractional structures[r]

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Stability criteria for linear Hamiltonian dynamic systems on time scales
Advances in Difference Equations 2011, 20[r]

(BQ) Part 1 book Partial differential equations in action has contents: Introduction, diffusion, the laplace equation, scalar conservation laws and first order equations, waves and vibrations.

(BQ) Part 1 book Partial differential equations in action has contents: Introduction, diffusion, the lapla[r]

and the self-adjoint condition RS ∗ SR ∗ 2 , Lemma 2 . 1 . A series of spectral results was obtained. We will remark that the boundary condition 1.8 includes the coupled boundary condition 1.2 when d 1, and the boundary conditions 1.4 when 1.6 holds. Agarwal and Wong studied existence of min[r]