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Local bifurcation from the second eigenvalue of the Laplacian in a square |
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| Authors: | Manuel del Pino Jorge Garcí a-Meliá n Monica Musso |
| Institution: | Departamento de Ingeniería Matemática and CMM, Universidad de Chile, Casilla 170 Correo 3, Santiago, Chile ; Departamento de Análisis Matemático, Universidad de La Laguna, c/ Astrofísico Fco. Sánchez S/N -- 38271 La Laguna, Spain ; Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi, 24 -- 10129 Torino, Italy |
| 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  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  . We also compute the Morse index of the solutions in the four branches. |
| Keywords: | Local bifurcation multiple branches double eigenvalue |
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