On Infinite Systems of Linear Differential Equations

1975 ◽  
Vol 27 (3) ◽  
pp. 691-703 ◽  
Author(s):  
J. P. McClure ◽  
R. Wong
Keyword(s):  
Differential Equations ◽  
Infinite System ◽  
Initial Conditions ◽  
Linear Differential Equations ◽  
Asymptotic Behavior Of Solutions ◽  
Complex Numbers ◽  
Infinite Matrix ◽  
Infinite Systems ◽  
Linear Differential ◽  
Image Position

Let A = [αtj] (i,j = 1, 2, …) be an infinite matrix with complex entries, and let z = (ζj) (j = 1, 2, …) be a sequence of complex numbers. In this paper we wish to investigate the existence, uniqueness and asymptotic behavior of solutions to the infinite system of linear differential equationswith the initial conditions

Infinite Systems of Differential Equations

1976 ◽  
Vol 28 (6) ◽  
pp. 1132-1145 ◽  
Author(s):  
J. P. McClure ◽  
R. Wong
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Nonlinear Equations ◽  
Asymptotic Behavior Of Solutions ◽  
Systems Of Nonlinear Equations ◽  
Infinite Systems ◽  
Systems Of Differential Equations ◽  
Constant Coefficients ◽  
Linear Differential ◽  
Image Position

In an earlier paper [7], we have studied the existence, uniqueness and asymptotic behavior of solutions to certain infinite systems of linear differential equations with constant coefficients. In the present paper we are interested in systems of nonlinear equations whose coefficients are not necessarily constants; more specifically, we are concerned with infinite systems of the form

scholarly journals The variational iteration method for solving n-th order fuzzy differential equations

Open Physics ◽  
2012 ◽  
Vol 10 (1) ◽  
Author(s):  
Hossein Jafari ◽  
Mohammad Saeidy ◽  
Dumitru Baleanu
Keyword(s):  
Differential Equations ◽  
Nonlinear Equations ◽  
Analytical Method ◽  
Iteration Method ◽  
Initial Conditions ◽  
Variational Iteration Method ◽  
Linear Differential Equations ◽  
Variational Iteration ◽  
Linear And Nonlinear ◽  
Linear Differential

AbstractThe variational iteration method (VIM) proposed by Ji-Huan He is a new analytical method for solving linear and nonlinear equations. In this paper, the variational iteration method has been applied in solving nth-order fuzzy linear differential equations with fuzzy initial conditions. This method is illustrated by solving several examples.

Solution Space Decompositions for nth Order Linear Differential Equations

1975 ◽  
Vol 27 (3) ◽  
pp. 508-512
Author(s):  
G. B. Gustafson ◽  
S. Sedziwy
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Equations ◽  
Solution Space ◽  
Decomposition Theorem ◽  
Linear Differential Equations ◽  
Direct Sum ◽  
Direct Sum Decomposition ◽  
Linear Differential ◽  
Image Position

Consider the wth order scalar ordinary differential equationwith pr ∈ C([0, ∞) → R ) . The purpose of this paper is to establish the following:DECOMPOSITION THEOREM. The solution space X of (1.1) has a direct sum Decompositionwhere M1 and M2 are subspaces of X such that(1) each solution in M1\﹛0﹜ is nonzero for sufficiently large t ﹛nono sdilatory) ;(2) each solution in M2 has infinitely many zeros ﹛oscillatory).

scholarly journals Solving Second-Order Linear Differential Equations with Random Analytic Coefficients about Regular-Singular Points

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 230
Author(s):  
Juan-Carlos Cortés ◽  
Ana Navarro-Quiles ◽  
José-Vicente Romero ◽  
María-Dolores Roselló
Keyword(s):  
Differential Equations ◽  
Initial Conditions ◽  
Random Variable ◽  
Second Order ◽  
Singular Points ◽  
Linear Differential Equations ◽  
Transformation Technique ◽  
Order Linear ◽  
Bessel Differential Equation ◽  
Linear Differential

In this contribution, we construct approximations for the density associated with the solution of second-order linear differential equations whose coefficients are analytic stochastic processes about regular-singular points. Our analysis is based on the combination of a random Fröbenius technique together with the random variable transformation technique assuming mild probabilistic conditions on the initial conditions and coefficients. The new results complete the ones recently established by the authors for the same class of stochastic differential equations, but about regular points. In this way, this new contribution allows us to study, for example, the important randomized Bessel differential equation.

scholarly journals The Elliptic Cylinder Functions of the Second Kind

1914 ◽  
Vol 33 ◽  
pp. 2-13 ◽  
Author(s):  
E. Lindsay Ince
Keyword(s):  
Differential Equation ◽  
General Solution ◽  
Differential Equations ◽  
Elliptic Cylinder ◽  
Linear Differential Equations ◽  
Periodic Functions ◽  
Linear Differential ◽  
Image Position

The differential equation of Mathieu, or the equation of the elliptic cylinder functionsis known by the theory of linear differential equations to have a general solution of the typeφ and ψ being periodic functions of z, with period 2π.

Oscillatory and asymptotic behaviour of all solutions of differential equations with deviating arguments

1978 ◽  
Vol 81 (3-4) ◽  
pp. 195-210 ◽  
Author(s):  
Ch. G. Philos
Keyword(s):  
Differential Equations ◽  
Asymptotic Behaviour ◽  
Unknown Function ◽  
Continuous Functions ◽  
Linear Differential Equations ◽  
Deviating Arguments ◽  
All Solutions ◽  
Non Linear ◽  
Linear Differential ◽  
Image Position

SynopsisThis paper deals with the oscillatory and asymptotic behaviour of all solutions of a class of nth order (n > 1) non-linear differential equations with deviating arguments involving the so called nth order r-derivative of the unknown function x defined bywhere r1, (i = 0,1,…, n – 1) are positive continuous functions on [t0, ∞). The results obtained extend and improve previous ones in [7 and 15] even in the usual case where r0 = r1 = … = rn–1 = 1.

scholarly journals Existence results for second order linear differential equations in Banach spaces

2018 ◽  
Vol 12 (2) ◽  
pp. 481-492
Author(s):  
M. Mursaleen ◽  
Syed Rizvi
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Infinite System ◽  
Second Order ◽  
Linear Differential Equations ◽  
Measures Of Noncompactness ◽  
Order Linear ◽  
Comparison Functions ◽  
Linear Differential ◽  
Convergent Sequences

In this paper we are concerned with the existence of solutions for certain classes of second order differential equations. First we deal with an infinite system of second order linear differential equations, which is reduced to an ordinary differential equation posed in the space of convergent sequences. Next we investigate the problem of existence for a second order differential equation posed on an arbitrary Banach space. The used approach is based on the measures of noncompactness concept, the use of Darbo's fixed point theorem and Kamke comparison functions.

Periodic Solutions by Picard's Approximations

1968 ◽  
Vol 11 (5) ◽  
pp. 743-745 ◽  
Author(s):  
T.A. Burton
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
General Framework ◽  
Floquet Theory ◽  
Linear Differential Equations ◽  
All Solutions ◽  
Private Correspondence ◽  
Linear Differential ◽  
Image Position

In [1] Demidovic considered a system of linear differential equationswith A(t) continuous, T-periodic, odd, and skew symmetric. He proved that all solutions of (1) are either T-periodic or 2T-periodic0 In [2] Epstein used Floquet theory to prove that all solutions of (1) are T-periodic without the skew symmetric hypothesis. Epstein's results were then generalized by Muldowney in [7] using Floquet theory. Much of the above work can also be interpreted as being part of the general framework of autosynartetic systems discussed by Lewis in [5] and [6]. According to private correspondence with Lewis it seems that he was aware of these results well before they were published. However, it appears that these theorems were neither stated nor suggested in the papers by Lewis.

scholarly journals On the non-existence of L2 solutions of a class of non-linear differential equations

1965 ◽  
Vol 14 (4) ◽  
pp. 257-268 ◽  
Author(s):  
J. Burlak
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Linear Differential Equations ◽  
Half Line ◽  
Non Linear ◽  
Linear Differential ◽  
Image Position

In 1950, Wintner (11) showed that if the function f(x) is continuous on the half-line [0, ∞) and, in a certain sense, is “ small when x is large ” then the differential equationdoes not have L2 solutions, where the function y(x) satisfying (1) is called an L2 solution if

Sign in / Sign up

Export Citation Format

Share Document