Gritsans, A.; Sadyrbaev, F. Nonlinear spectra: the Neumann problem. (English) Zbl 1177.34105 Math. Model. Anal. 14, No. 1, 33-42 (2009). The authors consider nonlinear equations of the form \[ x'' = - \lambda f (x^{+}) + \mu g (x^{-}), \]where \(\lambda\) and \(\mu\) are parameters, \(f,g : \mathbb{R}_{+} \longrightarrow \mathbb{R}_{+}\) are locally Lipschitz continuous functions such that \(f (0) = g (0) = 0, \;\;\;x^{+} : = \max \{x,0\}, \;\;x^{-} : = \max \{-x,0\}.\) Boundary conditions of the Neumann type, \(x'(a) = 0, \;\;x'(b) = 0\), are assumed. The authors describe values \((\lambda,\mu)\) for which such a problem has nontrivial solutions. The set of those pairs \((\lambda, \mu)\) are called the spectrum of the problem. Reviewer: Petru A. Cojuhari (Kraków) Cited in 1 Document MSC: 34L05 General spectral theory of ordinary differential operators 34B08 Parameter dependent boundary value problems for ordinary differential equations PDFBibTeX XMLCite \textit{A. Gritsans} and \textit{F. Sadyrbaev}, Math. Model. Anal. 14, No. 1, 33--42 (2009; Zbl 1177.34105) Full Text: DOI