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Nonlinear eigenvalue problems with the parameter near resonance. (English) Zbl 0724.34025
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)

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
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