In fluid field, Bernard [2] described the equations of motion for six velocity potentials of perfect fluids which led to a

variational principle that reproduced the Eulerian equation of motion.

Li and Song demonstrate how variational methods can be used in nonlinear differential equations, but begin by reviewing prerequisites such as Sobolev space and the

variational principle for readers who are a little rusty.

1] which is a more precise version of Ricceri's

Variational Principle [25, Theorem 2.

We shall do this by combining and extending two recent developments: a recent reformulation of the enhanced sampling problem into a powerful

variational principle that opens a wealth of possibilities and provides a novel and fruitful standpoint for new developments; and a procedure for extracting rates from enhanced runs.

Thus, referring to reference [3] 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.

We generalize Wheeler-Feynman electrodynamics [1,2] with a

variational principle whose extrema are required to satisfy a boundary-value problem [3,4].

Its

variational principle can be established using the semi-inverse method [27, 28]:

From the reduced

variational principle, [delta] [integral] <L> dz = 0 and Eq.

Key words: vibrations,

variational principle, displacements fields, connecting rod

These statements include the maximality results in Isac [13] and Nemeth [15]; which, in turn, extend Ekeland's

variational principle [7] (in short: EVP); so, it is natural to denote their union as (EVPv).

3] or [39]) and Ekeland's

Variational Principle (see, e.

By using the semi-inverse method [11] the

variational principle of the Eq.