Nondegeneracy of the second bifurcating branches for the Chafee-Infante problem on a planar symmetric domain

Author:
Yasuhito Miyamoto

Journal:
Proc. Amer. Math. Soc. **139** (2011), 975-984

MSC (2010):
Primary 35B32, 35P15; Secondary 35J61, 35J15

DOI:
https://doi.org/10.1090/S0002-9939-2010-10616-0

Published electronically:
July 30, 2010

MathSciNet review:
2745649

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a planar domain such that is symmetric with respect to both the - and -axes and satisfies certain conditions. Then the second eigenvalue of the Dirichlet Laplacian on , , is simple, and the corresponding eigenfunction is odd with respect to the -axis. Let be a function such that

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Additional Information

**Yasuhito Miyamoto**

Affiliation:
Department of Mathematics, Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8551, Japan

Email:
miyamoto@math.titech.ac.jp

DOI:
https://doi.org/10.1090/S0002-9939-2010-10616-0

Keywords:
Global branch,
bifurcation,
sign-changing solution,
planar symmetric domain,
second eigenvalue

Received by editor(s):
March 23, 2010

Published electronically:
July 30, 2010

Additional Notes:
This work was partially supported by Grant-in-Aid for Young Scientists (B) (Subject No. 21740116).

Communicated by:
Matthew J. Gursky

Article copyright:
© Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.