#### Glasnik Matematicki, Vol. 38, No.2 (2003), 285-298.

### PERIODIC SOLUTIONS OF A FIRST ORDER
DIFFERENTIAL EQUATION

### Lavoslav Čaklović

Department of Mathematics, University of Zagreb, P.O. Box 335,
10002 Zagreb, Croatia

*e-mail:* `caklovic@math.hr`

**Abstract.** The first order dynamical system
*z*' = *F*(*t,z*) is
considered, where *F* is *T*-periodic in time and sub-linear
at infinity. Existence of *T*-periodic solution is proved, using
degree theory, and applications to non-convex Hamiltonian systems
is given as well.

**2000 Mathematics Subject Classification.**
34C25, 46N20, 47H15, 55M25, 58C30, 58F22.

**Key words and phrases.** Differential equations, periodic solution, degree,
Hamiltonian system.

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