You know that the problem of calculus of variations is finding a y(x) for which [itex] \int_a^b L(x,y,y') dx [/itex] is stationary. I wanna know is it possible to solve this problem when L is a function of also y'' ? It happens e.g. in the variational method in quantum mechanics where we say that choosing any arbitrary wave function [itex] \psi(x) [/itex], the energy of the ground state of the system is always smaller than [itex] \int \psi^* H \psi dx [/itex]. But if we can find a [itex] \psi [/itex] for which this integral is stationary, then we have the wave function and also the energy of the ground state. But the problem is, for ordinary particle systems in non-relativistic quantum mechanics, H contains a second derivative.