Gossez, J.-P.; Marcos, A. On the first curve in the Fučik spectrum of a mixed problem. (English) Zbl 0912.35118 Caristi, Gabriella et al., Reaction diffusion systems. Papers from a meeting, Trieste, Italy, October 2–7, 1995. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 194, 157-162 (1998). The Fučík spectrum of the Laplacian under mixed boundary conditions is defined as the set \(\sum'\) of those \((\alpha,\beta)\in\mathbb R^2\) such that \[ -\Delta u = \alpha u^+ - \beta u^- \quad \text{in} \;\Omega,\qquad u=0 \text{ on} \;\Gamma_1,\quad \partial u/\partial n = 0 \text{ on }\Gamma_2 \] has a non-trivial solution \(u\). Here \(\partial/\partial n\) denotes the exterior normal derivative. In this paper a curve in the \(\alpha\beta\) plane is constructed which belongs to \(\sum'\) and which generalizes the second eigenvalue of the Laplacian subject to the mixed boundary conditions.For the entire collection see [Zbl 0873.00023]. Reviewer: P.Drábek (Praha) Cited in 1 Document MSC: 35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs 35J65 Nonlinear boundary value problems for linear elliptic equations Keywords:generalized eigenvalue problem; mixed boundary value problem PDFBibTeX XMLCite \textit{J. P. Gossez} and \textit{A. Marcos}, Lect. Notes Pure Appl. Math. 194, 157--162 (1998; Zbl 0912.35118)