In the context of variational calculus, what is meant by 'Lyapunov functional'?
Frankly speaking, in calculus of variation, we are searching for some $u(x)$ to put in $F(x,u(x),u'(x))$ in order to minimize $$ J(u):=\int_a^b F(x,u(x),u'(x))\, dx. $$
But what is meant by 'Lyapunov functional' in this context?