How can I be sure that the action has a minimum?

[alialice]

When you write an action and then you calculate its minima, how can you be sure that they are minima and not maxima?
Thanks

 

[G01]

Usually the phrase, "minimizing the action" is somewhat misused and can make things confusing for this reason. Finding the "extreme points" or "stationary points" of the action is what is important. The "principle of least action" is more accurately termed the "principle of stationary action."

For instance, in Lagrangian Mechanics, any path that extremizes the action, i.e. $\delta S=0$, whether minima or maxima, will be a solution to the Euler-Lagrange equation.

 

[andrien]

If the initial and final points are fixed,then action does have a minimum for the correct classical path.But I will have to see a book before conforming it.