In this paper we present some results on the Fučík spectrum for the Laplace operator, that give new information on its structure. In particular, these results show that, if Ω is a bounded domain of R^N with N>1, then the Fučík spectrum has infinitely many curves asymptotic to the lines {λ_1}×R and R×{λ_1}, where λ_1 denotes the first eigenvalue of the operator −Δ in H_0^1(Ω). Notice that the situation is quite different in the case N=; in fact, in this case the Fučík spectrum may be obtained by direct computation and one can verify that it includes only two curves asymptotic to these lines.
Molle, R., Passaseo, D. (2015). Infinitely many new curves of the Fučík spectrum. ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE, 32(6), 1145-1171 [10.1016/j.anihpc.2014.05.007].
Infinitely many new curves of the Fučík spectrum
MOLLE, RICCARDO
;
2015-11-01
Abstract
In this paper we present some results on the Fučík spectrum for the Laplace operator, that give new information on its structure. In particular, these results show that, if Ω is a bounded domain of R^N with N>1, then the Fučík spectrum has infinitely many curves asymptotic to the lines {λ_1}×R and R×{λ_1}, where λ_1 denotes the first eigenvalue of the operator −Δ in H_0^1(Ω). Notice that the situation is quite different in the case N=; in fact, in this case the Fučík spectrum may be obtained by direct computation and one can verify that it includes only two curves asymptotic to these lines.| File | Dimensione | Formato | |
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