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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Local bifurcation from the second eigenvalue of the Laplacian in a square


Authors: Manuel del Pino, Jorge García-Melián and Monica Musso
Journal: Proc. Amer. Math. Soc. 131 (2003), 3499-3505
MSC (2000): Primary 35B32, 35J25
Published electronically: April 1, 2003
MathSciNet review: 1991761
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Abstract: In this work we study local bifurcation from the branch of trivial solutions for a class of semilinear elliptic equations, at the second eigenvalue $\lambda_2$ of a square. We find that the bifurcation set can be locally described as the union of exactly four bifurcation branches of nontrivial solutions which cross the bifurcation point $(\lambda_2,0)$. We also compute the Morse index of the solutions in the four branches.


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Additional Information

Manuel del Pino
Affiliation: Departamento de Ingeniería Matemática and CMM, Universidad de Chile, Casilla 170 Correo 3, Santiago, Chile
Email: delpino@dim.uchile.cl

Jorge García-Melián
Affiliation: Departamento de Análisis Matemático, Universidad de La Laguna, c/ Astrofísico Fco. Sánchez S/N – 38271 La Laguna, Spain
Email: jjgarmel@ull.es

Monica Musso
Affiliation: Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi, 24 – 10129 Torino, Italy
Email: musso@calvino.polito.it

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06906-5
PII: S 0002-9939(03)06906-5
Keywords: Local bifurcation, multiple branches, double eigenvalue
Received by editor(s): June 2, 2002
Published electronically: April 1, 2003
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2003 American Mathematical Society