Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If you need an accessible version of this item please contact JSTOR User Support

Second-Order Differential Equations with Fractional Transition Points

F. W. J. Olver
Transactions of the American Mathematical Society
Vol. 226 (Feb., 1977), pp. 227-241
DOI: 10.2307/1997952
Stable URL: http://www.jstor.org/stable/1997952
Page Count: 15
  • Read Online (Free)
  • Download ($30.00)
  • Subscribe ($19.50)
  • Cite this Item
If you need an accessible version of this item please contact JSTOR User Support
Second-Order Differential Equations with Fractional Transition Points
Preview not available

Abstract

An investigation is made of the differential equation $$d^2w/dx^2 = \{u^2(x - x_0)^\lambda f(u, x) + g(u, x)/(x - x_0)^2\}w$$, in which $u$ is a large real (or complex) parameter, $\lambda$ is a real constant such that $\lambda > -2, x$ is a real (or complex) variable, and $f(u, x)$ and $g(u, x)$ are continuous (or analytic) functions of $x$ in a real interval (or complex domain) containing $x_0$. The interval (or domain) need not be bounded. Previous results of Langer and Riekstiņš giving approximate solutions in terms of Bessel functions of order $1/(\lambda + 2)$ are extended and error bounds supplied.

Page Thumbnails

  • Thumbnail: Page 
227
    227
  • Thumbnail: Page 
228
    228
  • Thumbnail: Page 
229
    229
  • Thumbnail: Page 
230
    230
  • Thumbnail: Page 
231
    231
  • Thumbnail: Page 
232
    232
  • Thumbnail: Page 
233
    233
  • Thumbnail: Page 
234
    234
  • Thumbnail: Page 
235
    235
  • Thumbnail: Page 
236
    236
  • Thumbnail: Page 
237
    237
  • Thumbnail: Page 
238
    238
  • Thumbnail: Page 
239
    239
  • Thumbnail: Page 
240
    240
  • Thumbnail: Page 
241
    241