Prescribing, by conformal transformation, the k-elementary symmetric polynomial of the Schouten tensor σk(P) to be constant is a generalisation of the Yamabe problem. On compact Riemannian n-manifolds we show that, for 3 ≤ k ≤ n, this prescription equation is an Euler-Lagrange equation of some action if and only if the structure is locally conformally flat.

A kinematical study is made on the relation between the spin-singlet and spin-triplet pair distribution functions in the many-body system of spin-1/2 particles, and a group of inequalities is derived from the positiveness of the square of the "local spin" which is the total spin of a subsystem confined in a certain local region. This spin condition is applied to the neutron matter in the two-bo...

Based on the modified Landau-Lifshitz-Gilbert equation for an arbitrary Stoner particle under an external magnetic field and a spin-polarized electric current, differential equations for the optimal reversal trajectory, along which the magnetization reversal is the fastest one among all possible reversal routes, are obtained. We show that this is a Euler-Lagrange problem with constrains. The Eu...

Some new global results are given about solutions to the boundary value problem for the Euler-Lagrange equations for the Ginzburg-Landau model of a one-dimensional superconductor. The main advance is a proof that in some parameter range there is a branch of asymmetric solutions connecting the branch of symmetric solutions to the normal state. Also, simplified proofs are presented for some local...

using fixed point method, we prove some new stability results for lie $(alpha,beta,gamma)$-derivations and lie $c^{ast}$-algebra homomorphisms on lie $c^{ast}$-algebras associated with the euler-lagrange type additive functional equation begin{align*} sum^{n}_{j=1}f{bigg(-r_{j}x_{j}+sum_{1leq i leq n, ineq j}r_{i}x_{i}bigg)}+2sum^{n}_{i=1}r_{i}f(x_{i})=nf{bigg(sum^{n}_{i=1}r_{i}x_{i}bigg)} end{...

In the theory of mathematical optimization one try to find maximum or minimum points of functions depending of real variables and of other functions. Optimal control theory is a modern extension of the classical calculus of variations. Euler and Lagrange developed the theory of the calculus of variations in the eighteenth century. Its main ingredient is the Euler equation which was discovered a...

Variational problems under uniform quasiconvex constraints on the gradient are studied. Our technique consists in approximating the original problem by a one−parameter family of smooth unconstrained optimization problems. Existence of solutions to the problems under consideration is proved as well as existence of lagrange multipliers associated to the uniform constraint; no constraint qualifica...

The case when a partial differential equation (PDE) can be considered as an Euler-Lagrange (E-L) equation of an energy functional, consisting of a data term and a smoothness term is investigated. We show the necessary conditions for a PDE to be the E-L equation for a corresponding functional. This energy functional is applied to a color image denoising problem and it is shown that the method co...

Recent success in nonlinear control design is applied to the control of Euler–Lagrange systems. It is known that the existence of optimal control depends on solvability of the so-called Hamilton–Jacobi–Isaccs (HJI) partial differential equation. In this article, the associated HJI equation for nonlinear inverse-optimal control problem for Euler–Lagrangian system is solved analytically. The resu...