# No Constant Solution => No periodic solution

1. Oct 3, 2010

### cacosomoza

Shall f be continous function of two real variables. Proof that if equation x''=f(x,x') has not constant solutions, then neither it has periodic solutions.

2. Oct 4, 2010

### Eynstone

This follows fom the Poincare-Bendixon theorem : a closed orbit must enclose a stationary point.