Infinitely many new curves of the Fucik spectrum

摘要

In this paper we present some results on the Falk spectrum for the Laplace operator, that give new information on its structure. In particular, these results show that, if Omega is a bounded domain of R-N with N > 1, then the Fucik spectrum has infinitely many curves asymptotic to the lines {lambda(1)} x R and R x {lambda(1)}, where lambda(1) denotes the first eigenvalue of the operator -Delta in H-0(1)(Omega). Notice that the situation is quite different in the case N = 1; in fact, in this case the RIM spectrum may be obtained by direct computation and one can verify that it includes only two curves asymptotic to these lines. (C) 2014 Elsevier Masson SAS. All rights reserved.