# Requirements of a functional

what are the requirements of a functional J[y] to exist in the form that its minimum will yield to a differential equation?..i mean let be the functional with condition:

$$J[y]=\int_{a}^{b}dx(p(x)(y`)^{2}+V(x)y^{2})$$

$$\int_{a}^{b}y^{2}dx=C$$ with c a constant...

then what conditions should p and V(x) function fulfill in order to the functional have an extremum?..