What does it mean that boundary terms vanish in Partial Differential Equations?

Question

While reading Haberman's Applied Partial Differential Equations, the topic on self-adjointness, what does it mean that "boundary terms vanish"?

More context:

"Supposed that u and v are any two functions, but with the restriction that the boundary terms happen to vanish":

$p(u\displaystyle\frac{dv}{dx} - v\displaystyle\frac{du}{dx})\Big|_a^b \ = 0$

Answer 1

"vanish" just means it evaluates to zero, i.e.

$$ u(a) = u(b) = 0 $$ $$ v(a) = v(v) = 0 $$