Abstract.
The existence, non-existence and multiplicity of solutions to periodic boundary value problems
is discussed, where \(\phi : (-a, a)\rightarrow {\mathbb{R}}\) or \(\phi : {\mathbb{R}}\rightarrow (-a, a)\) is an increasing homeomorphism such that \(\phi (0) = 0\) and \(0 < a \leq \infty\). The nonlinear term g is assumed to be bounded, positive and \(g(\pm\infty) = 0\).
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Bereanu, C., Mawhin, J. Multiple periodic solutions of ordinary differential equations with bounded nonlinearities and ϕ-Laplacian. Nonlinear differ. equ. appl. 15, 159–168 (2008). https://doi.org/10.1007/s00030-007-7004-x
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DOI: https://doi.org/10.1007/s00030-007-7004-x