Multiple periodic solutions of ordinary differential equations with bounded nonlinearities and \(\varphi\)-Laplacian (Q927383)

The authors generalize some existence and multiplicity results on periodic solutions previously established for second order ODE's to equations involving the so-called \(\phi\)-Laplacian. Precisely, the second derivative \(u''\) in the differential equation is replaced by \((\phi(u'))'\), where \(\phi: (-a,a) \to R\) or \(\phi: R \to (-a,a)\) is an increasing homeomorphism such that \(\phi(0)=0\), and \(0 < a \leq \infty\). Depending on the value of a parameter \(s\), they prove that their periodic problem has no solutions, one solution, or two solutions.