These are based on either Dyson-Schwinger equations [2-7] or functional renormalization group flow equations [8, 9], or they exploit the variational principle
in either the Hamiltonian [10, 11] or covariant [12, 13] formulation of gauge theory.
Blum and Elze studied the semiquantum chaos in a double-well potential with the time dependence of variational principle
Based on the elastic variational principle
, the governing equation is as follows:
It is worth mentioning that Caristi's fixed point theorem is equivalent to the Ekeland variational principle
In  a variational principle
for Lagrangian densities containing derivatives of real order was formulated and the invariance of this principle is studied in two characteristic cases.
 Bernard.f.Schutz, (1970), Perfect Fluid in General Relativity: Velocity Potentials and a Variational Principle
Lemma 4 (Ekeland's variational principle
; see ).
Of course the first integrals we have found here from a variational principle
all satisfy (33a) and (33b).
In the present paper, using a smooth version of [8, Theorem 2.1] which is a more precise version of Ricceri's Variational Principle
[25, Theorem 2.5], requiring that the nonlinear term f has a suitable oscillating behavior at infinity, we establish the existence of a precise interval A such that for every [lambda] [member of] [LAMBDA] and for every [L.sup.2]-Caratheodory function g satisfying a certain growth at infinity, choosing [mu] sufficiently small, the problem (1.1) admits a sequence of generalized solutions which is unbounded in the space E which will be introduced later (Theorem 3.1).
Thus, referring to reference  for applying least square method to establish "partial and temporary unified theory of natural science so far" including all the equations of natural science so far (in which, the theory of everything to express all of natural laws, described by Hawking that a single equation could be written on a T-shirt, is partially and temporarily realized in the form of "partial and temporary unified variational principle
of natural science so far"), Eq.(5) (one kind of "certainty-uncertainty principles" with general form) can be restricted (or constrained) by principle (law) of conservation of energy as follows