Infinitely many nonradial solutions to a superlinear Dirichlet problem

Authors:
Hugo Aduén and Alfonso Castro

Journal:
Proc. Amer. Math. Soc. **131** (2003), 835-843

MSC (2000):
Primary 35J20; Secondary 34B15

Published electronically:
September 17, 2002

MathSciNet review:
1937421

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this article we provide sufficient conditions for a superlinear Dirichlet problem to have infinitely many nonradial solutions. Our hypotheses do not require the nonlinearity to be an odd function. For the sake of simplicity in the calculations we carry out details of proofs in a ball. However, the proofs go through for any annulus.

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Additional Information

**Hugo Aduén**

Affiliation:
Departamento de Matemáticas, Universidad de Córdoba, Montería, Colombia

Email:
haduen@hotmail.com

**Alfonso Castro**

Affiliation:
Division of Mathematics and Statistics, The University of Texas at San Antonio, San Antonio, Texas 78249

Email:
acastro@utsa.edu

DOI:
http://dx.doi.org/10.1090/S0002-9939-02-06642-X

Keywords:
Critical point,
Morse index,
nonradial solutions,
Cwikel inequality,
nonlinear elliptic equation

Received by editor(s):
March 8, 2001

Received by editor(s) in revised form:
October 15, 2001

Published electronically:
September 17, 2002

Communicated by:
David S. Tartakoff

Article copyright:
© Copyright 2002
American Mathematical Society