Fixed Points of ODE: Clarifying Conditions

Apteronotus
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In a book on synchronization it is stated that given the ODE

\frac{d\psi}{dt}=-\nu+\epsilon q(\psi)

there is at least one pair of fixed points if

\epsilon q_{min}<\nu<\epsilon q_{max}

were q_{min}, q_{max} are the min and max values of q(\psi) respectively.

While this could be true under particular circumstances (ie. when q_{min}<0, q_{max}>0), I don't see how it could hold in general; such as the case when q(\psi)>0.

Can anyone shed some light on this?

Thanks in advance.
 
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Just think about this...

<br /> 0 = -\nu+\epsilon q(\psi)<br />
 
Assuming that q is continuous, the "intermediate value property" gives the answer.
 
Yes, of course! Thank you both.
 
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