Morse index and uniqueness for positive solutions of radial -Laplace equations
Authors:
Amandine Aftalion and Filomena Pacella
Journal:
Trans. Amer. Math. Soc. 356 (2004), 4255-4272
MSC (2000):
Primary 58E05, 35J05
DOI:
https://doi.org/10.1090/S0002-9947-04-03628-1
Published electronically:
June 2, 2004
MathSciNet review:
2067118
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We study the positive radial solutions of the Dirichlet problem in
,
in
,
on
, where
,
, is the
-Laplace operator,
is the unit ball in
centered at the origin and
is a
function. We are able to get results on the spectrum of the linearized operator in a suitable weighted space of radial functions and derive from this information on the Morse index. In particular, we show that positive radial solutions of Mountain Pass type have Morse index 1 in the subspace of radial functions of
. We use this to prove uniqueness and nondegeneracy of positive radial solutions when
is of the type
and
.
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Additional Information
Amandine Aftalion
Affiliation:
Laboratoire Jacques-Louis Lions, B.C. 187, Université Paris 6, 175 rue du Chevaleret, 75013 Paris, France
Email:
aftalion@ann.jussieu.fr
Filomena Pacella
Affiliation:
Dipartimento di Matematica, Università di Roma “La Sapienza", P.le A. Moro 2, 00185 Roma, Italy
Email:
pacella@mat.uniroma1.it
DOI:
https://doi.org/10.1090/S0002-9947-04-03628-1
Received by editor(s):
May 23, 2002
Published electronically:
June 2, 2004
Additional Notes:
Research of the second author was supported by MIUR, project “Variational methods and Nonlinear Differential Equations”
Article copyright:
© Copyright 2004
American Mathematical Society