Mawhin, Jean; Schmitt, Klaus Nonlinear eigenvalue problems with the parameter near resonance. (English) Zbl 0724.34025 Ann. Pol. Math. 51, 241-248 (1990). Nonlinear Sturm-Liouville problems subject to either periodic or Dirichlet boundary conditions are investigated. The nonlinear perturbation term is bounded and satisfies a sign condition. By Leray- Schauder degree theory it can be shown that close to the principal eigenvalue of the linear part either one or three solutions exist. Reviewer: A.Steindl (Wien) Cited in 2 ReviewsCited in 32 Documents MSC: 34B15 Nonlinear boundary value problems for ordinary differential equations 34B24 Sturm-Liouville theory 34C23 Bifurcation theory for ordinary differential equations 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations 34C25 Periodic solutions to ordinary differential equations Keywords:Nonlinear Sturm-Liouville problems; Leray-Schauder degree theory PDFBibTeX XMLCite \textit{J. Mawhin} and \textit{K. Schmitt}, Ann. Pol. Math. 51, 241--248 (1990; Zbl 0724.34025) Full Text: DOI