Stable and finite Morse index solutions on or on bounded domains with small diffusion
Author:
E. N. Dancer
Journal:
Trans. Amer. Math. Soc. 357 (2005), 1225-1243
MSC (2000):
Primary 35B35
DOI:
https://doi.org/10.1090/S0002-9947-04-03543-3
Published electronically:
September 2, 2004
MathSciNet review:
2110438
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: In this paper, we study bounded solutions of on
(where
and sometimes
) and show that, for most
's, the weakly stable and finite Morse index solutions are quite simple. We then use this to obtain a very good understanding of the stable and bounded Morse index solutions of
on
with Dirichlet or Neumann boundary conditions for small
.
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Additional Information
E. N. Dancer
Affiliation:
School of Mathematics and Statistics, University of Sydney, New South Wales 2006, Australia
DOI:
https://doi.org/10.1090/S0002-9947-04-03543-3
Received by editor(s):
July 26, 2002
Received by editor(s) in revised form:
October 21, 2003
Published electronically:
September 2, 2004
Article copyright:
© Copyright 2004
American Mathematical Society