Definition:Conjugate Point (Calculus of Variations)

Also defined as
In the context of Calculus of Variations, functionals are one of the most important concepts.

Therefore, instead of a function, a functional which is minimised by the given function is used as a concept of reference.

Then, if $\tilde a$ is conjugate to $a$ solution of $\paren {-\map {\dfrac \d {\d x} } {P h'} + Q h = 0}$, then it is also conjugate  $\ds \int_a^b \paren {P h'^2 + Q h^2} \rd x$.