## 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

### Keywords:

positive periodic solution; cone; fixed-point index
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