Sentence examples for using the least action from inspiring English sources

These equations are formulated using the least action principle.

First, using the least action principle in critical point theory, we get the first main result.

Using the least action principle, the existence of periodic solutions for some nonautonomous second order Hamiltonian systems is obtained.

The following main results are obtained by using the least action principle and by the minimax methods.

Some existence and multiplicity results of solutions are given by using the least action principle and minmax methods in nonsmooth critical point theory.

They give two existence results of solutions for the above system by using the least action principle and mountain pass theorem in critical point theory.

In [5], Pu et al. used the least action principle, the Ekeland variational principle and the mountain pass theorem to prove the existence and multiplicity of solutions of (1) when (g x,u =a(x)|u|^{s-2}u+f x,u)) ((ain L^{infty}(varOmega )), (sin(1,2)) and (fin C(overline{varOmega }timesmathbb{R},mathbb{R}))).

Together, these conditions ensure that, when individual interests are violated by a public health action, the action will likely achieve public health benefits that outweigh the violated interests, using the least invasive methods available.

Very recently, in [35], Kuang investigated the following second order Hamiltonian system: ddot{u}(t)=nabla Fbigl t,u(t bigr),quad tinmathbb{R}, (1.2) and obtained two existence results of weak quasi-periodic solutions for system (1.2) by making use of the least action principle and the saddle point theorem, respectively.

To the best of our knowledge, there is no paper discussing the subharmonics solutions of p-Laplacian system by using the dual least action principle.

The disintegration paths are obtained from the least action principle.