scholarly journals Characterization for Rectifiable and Nonrectifiable Attractivity of Nonautonomous Systems of Linear Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Yūki Naito ◽  
Mervan Pašić
Keyword(s):  
Differential Equations ◽  
Asymptotic Behaviour ◽  
Zero Solution ◽  
Nonautonomous System ◽  
Linear Differential Equations ◽  
Solution Curve ◽  
Nonautonomous Systems ◽  
Polynomial Coefficients ◽  
The Matrix ◽  
Linear Differential

We study a new kind of asymptotic behaviour near for the nonautonomous system of two linear differential equations: , , where the matrix-valued function has a kind of singularity at . It is called rectifiable (resp., nonrectifiable) attractivity of the zero solution, which means that as and the length of the solution curve of is finite (resp., infinite) for every . It is characterized in terms of certain asymptotic behaviour of the eigenvalues of near . Consequently, the main results are applied to a system of two linear differential equations with polynomial coefficients which are singular at .

A Recursion Formula for the Coefficients of Entire Functions Satisfying an ODE with Polynomial Coefficients

2004 ◽  
Vol 11 (3) ◽  
pp. 409-414
Author(s):  
C. Belingeri
Keyword(s):  
Differential Equations ◽  
Sum Rules ◽  
Entire Functions ◽  
Recursion Formula ◽  
Linear Differential Equations ◽  
Bell Polynomials ◽  
Polynomial Coefficients ◽  
Linear Differential

Abstract A recursion formula for the coefficients of entire functions which are solutions of linear differential equations with polynomial coefficients is derived. Some explicit examples are developed. The Newton sum rules for the powers of zeros of a class of entire functions are constructed in terms of Bell polynomials.

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 Dwork’s conjecture on the logarithmic growth of solutions of p-adic differential equations

2008 ◽  
Vol 144 (2) ◽  
pp. 484-494 ◽  
Author(s):  
Yves André
Keyword(s):  
Differential Equations ◽  
Asymptotic Behaviour ◽  
Linear Differential Equations ◽  
Asymptotic Behaviour Of Solutions ◽  
Linear Differential ◽  
Growth Of Solutions ◽  
Logarithmic Growth

AbstractThis is a study of the asymptotic behaviour of solutions of p-adic linear differential equations near the boundary of their convergence disks. We prove Dwork’s conjecture on the logarithmic growth of solutions in generic versus special disks.

scholarly journals info geting lost in plates 7u,8,9,11 and 13 - I. On the normal series satisfying linear differential equations

1906 ◽  
Vol 205 (387-401) ◽  
pp. 1-35 ◽  
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Equations ◽  
London Mathematical Society ◽  
Linear Ordinary Differential Equation ◽  
Linear Differential Equations ◽  
Independent Variables ◽  
Normal Series ◽  
The Matrix ◽  
Linear Differential

1. The present paper is suggested by that of Dr. H. F. Baker in the ‘Proceedings of the London Mathematical Society,’ vol. xxxv., p. 333, “On the Integration of Linear Differential Equations.” In that paper a linear ordinary differential equation of order n is considered as derived from a system of n linear simultaneous differential equations dx i / dt = u i1 x +.....+ u i n x n ( i = 1... n ), or, in abbreviated notation, dx / dt = ux , where u is a square matrix of n rows and columns whose elements are functions of t , and x denotes a column of n independent variables. A symbolic solution of this system is there given and denoted by the symbol Ω( u ). This is a matrix of n rows and columns formed from u as follows :—Q ( ϕ ) is the matrix of which each element is the t -integral from t 0 to t of the corresponding element of ϕ , ϕ being any matrix of n rows and columns; then Ω( u ) = 1+Q u +Q u Q u +Q u Q u Q u ..... ad inf ., where the operator Q affects the whole of the part following it in any term.

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