UNIQUENESS OF POSITIVE RADIAL SOLUTIONS OF DELTA-U+F(U)=0 IN R(N) .2.

Authors
MCLEOD K
Citation
K. Mcleod, UNIQUENESS OF POSITIVE RADIAL SOLUTIONS OF DELTA-U+F(U)=0 IN R(N) .2., Transactions of the American Mathematical Society, 339(2), 1993, pp. 495-505
Citations number
11
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Transactions of the American Mathematical Society → ACNP
ISSN journal
00029947
Volume
339
Issue
2
Year of publication
1993
Pages
495 - 505
Database
ISI
SICI code
0002-9947(1993)339:2<495:UOPRSO>2.0.ZU;2-2
Abstract
We prove a uniqueness result for the positive solution of DELTAu + f(u ) = 0 in R(n) which goes to 0 at infinity. The result applies to a wid e class of nonlinear functions f, including the important model case f (u) = - u + u(p), 1 < p < (n + 2)/(n - 2). The result is proved by red ucing to an initial-boundary problem for the ODE u'' + (n - 1)/r + f(u ) = 0 and using a shooting method.