Data di Pubblicazione:
2009
Citazione:
On the Fucik spectrum of the Laplacian on a torus / E. Massa, B. Ruf. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - 256:5(2009), pp. 1432-1452.
Abstract:
We study the \fuc spectrum of the Laplacian on a two-dimensional torus T^2. Exploiting the invariance properties of the domain T^2 with respect to translations we obtain a good description of large parts of the
spectrum. In particular, for each eigenvalue of the Laplacian we will find an explicit global curve in the Fucik spectrum which passes through this eigenvalue; these curves are ordered, and we will show that their asymptotic limits are positive. On the other hand, using a topological index based on the mentioned group invariance, we will obtain a variational characterization of global curves in the Fucik spectrum; also these curves emanate from the eigenvalues of the Laplacian, and we will show that they tend asymptotically to zero. Thus, we infer that the variational and the explicit curves cannot coincide globally, and that in fact many curve crossings must occur. We will give a bifurcation result which partially explains these phenomena.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Fučík spectrum; Geometrical T2-index; Secondary bifurcation; Variational characterization
Elenco autori:
E. Massa, B. Ruf
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