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

del Pino, Manuel; García-Melián, Jorge; Musso, Monica

doi:10.1090/S0002-9939-03-06906-5

Local bifurcation from the second eigenvalue of the Laplacian in a square
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by Manuel del Pino, Jorge García-Melián and Monica Musso

Proc. Amer. Math. Soc. 131 (2003), 3499-3505

DOI: https://doi.org/10.1090/S0002-9939-03-06906-5

Published electronically: April 1, 2003

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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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