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Positive periodic solutions of first and second order ordinary differential equations. (English) Zbl 1073.34041

The paper deals with the existence of positive \(\omega\)-periodic solutions of the second-order differential equation \[ -u^{\prime \prime}(t) = f(t,u(t)), \quad t \in \mathbb{R}, \] as well as first-order ordinary differential equations. The main tool is the fixed-point index theory in cones.

MSC:

34C25 Periodic solutions to ordinary differential equations
47H10 Fixed-point theorems
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
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