Extension of Euler Lagrange identity by superquadratic power functions

Variational Problems with Fractional Derivatives: Euler-Lagrange Equations

We generalize the fractional variational problem by allowing the possibility that the lower bound in the fractional derivative does not coincide with the lower bound of the integral that is minimized. Also, for the standard case when these two bounds coincide, we derive a new form of Euler-Lagrange equations. We use approximations for fractional derivatives in the Lagrangian and obtain the Euler-Lagrange equations which approximate the initial Euler-Lagrange equations in a weak sense.

Stability of Euler-Lagrange type cubic functional equations in quasi-Banach spaces

In this paper, we study the generalized Hyers-Ulam stability of Euler-Lagrange type cubic functional equation of the form \begin{align*} 2mf(x + my) + 2f(mx - y) = (m^3 + m)[f(x+ y) + f(x - y)] + 2(m^4 - 1)f(y) \end{align*} for all $x,y \in X$, where $m$ is a fixed scalar such that $m \neq 0,1$, and $f$ is a map from a quasi-normed space $X$ to a quasi-Banach space $Y$ over the same field with $X$ by applying the alternative fixed point theorem.

Generalization of Euler-Lagrange Equations to Find Min-max Optimal Solution of Uncertain Systems

In this paper, calculus of variation methods are generalized to find min-max optimal solution of uncertain dynamical systems with uncertain or certain cost. First, a new form of Euler-Lagrange conditions for uncertain systems is presented. Then several cases are indicated where final condition can be specified or free. Also necessary conditions are introduced to existence of min-max optimal solution of the uncertain systems. Finally, efficiency of the proposed method is verified through some examples.

Euler-Lagrange equations for functionals defined on Fréchet manifolds

We prove a version of the variational Euler-Lagrange equations valid for functionals defined on Fréchet manifolds, such as the spaces of sections of differentiable vector bundles appearing in various physical theories.

Hadamard与Vandermonde行列式及Bernoulli-Euler-Lagrange-Aitken-Nikiporets型多项式求根数值方法

Hadamard and Vandermonde determinants and Bernoulli-Euler-Lagrange-Aitken-Nikiporets type numerical method for roots of polynomials

本文发展了Euler-Lagrange方法，通过计算由函数$P'(z)/P(z)$的Taylor和Laurent级数系数构建的Hadamard行列式之比的极限，求解任意复多项式的所有根。