A remark on an irregular singular point of the second order linear differential equation
نویسندگان
چکیده
منابع مشابه
A RESEARCH NOTE ON THE SECOND ORDER DIFFERENTIAL EQUATION
Let U(t, ) be solution of the Dirichlet problem y''+( t-q(t))y= 0 - 1 t l y(-l)= 0 = y(x), with variabIe t on (-1, x), for fixed x, which satisfies the initial condition U(-1, )=0 , (-1, )=1. In this paper, the asymptotic representation of the corresponding eigenfunctions of the eigen values has been investigated . Furthermore, the leading term of the asymptotic formula for ...
متن کاملOn the stability of linear differential equations of second order
The aim of this paper is to investigate the Hyers-Ulam stability of the linear differential equation$$y''(x)+alpha y'(x)+beta y(x)=f(x)$$in general case, where $yin C^2[a,b],$ $fin C[a,b]$ and $-infty
متن کاملOn Singular Solutions of a Second Order Differential Equation
In the paper, sufficient conditions are given under which all nontrivial solutions of (g(a(t)y))+r(t)f(y) = 0 are proper where a > 0, r > 0, f(x)x > 0, g(x)x > 0 for x 6= 0 and g is increasing on R. A sufficient condition for the existence of a singular solution of the second kind is given.
متن کاملSecond-order linear differential equations with two irregular singular points of rank three: the characteristic exponent
Abstract For a second-order linear differential equation with two irregular singular points of rank three, multiple Laplace-type contour integral solutions are considered. An explicit formula in terms of the Stokes multipliers is derived for the characteristic exponent of the multiplicative solutions. The Stokes multipliers are represented by converging series with terms for which limit formula...
متن کاملAsymptotic Solution with Respect to a Parameter of a Differential Equation Having an Irregular Singular Point
with v — 2 a positive real constant. The complex variable z is to be confined to a bounded neighborhood of the irregular singular point Zo. The analogous problem for a class of wth order differential equations, containing (1) for integral ^5:6, has been discussed by Hurd [2]. His analysis is somewhat complicated, and it appears that a clearer and more direct investigation of the asymptotic solu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Kodai Mathematical Journal
سال: 1961
ISSN: 0386-5991
DOI: 10.2996/kmj/1138844367