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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
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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

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

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