Results 1 to 10 of about 3,059 (201)

On the validity of the Euler–Lagrange equation

Journal of Mathematical Analysis and Applications, 2005
The authors deal with the variational problem \[ J(x)=\int^b_aL\bigl (t,x(t),x'(t)\bigr)\,dt\to\min\quad \bigl(x(a)=A,x(b)=B\bigr) \] in the space \(M\) of absolutely continuous vector-valued functions \(x(t)\in \mathbb{R}^n\) \((a\leq t\leq b)\). Let \(\widehat x(t)\) be a local weak minimizer. Assumptions: (i) \(\nabla_xL(.,\widehat x(.),\widehat x'(.
A. FERRIERO, MARCHINI, ELSA MARIA
exaly   +4 more sources

Some new discretizations of the Euler–Lagrange equation

Communications in Nonlinear Science and Numerical Simulation, 2021
Publicaci?n en abierto financiada por la Universidad de Salamanca como participante en el Acuerdo Transformativo CRUE-CSIC con Elsevier, 2021 ...
Mihaela Popescu, Higinio Ramos, M Popescu   +2 more
exaly   +4 more sources

On the Validity of the Euler–Lagrange Equation

Journal of Differential Equations, 2001
The paper concerns the following minimization problem \[ \text{Min } \int_\Omega [f(\|\nabla u(x)\|)+ g(x,u(x))] dx,\quad u- u^0\in W^0\in W^{1,1}_0(\Omega), \] where \(\Omega\) is an open bounded domain with Lipschitz boundary, \(W^0\) is a linear subset of \(W^{1,1}_0(\Omega)\) which contains all \(w\in W^{1,1}\) with \(\int_\Omega f(\|\nabla w(x)\|)
Arrigo Cellina
exaly   +2 more sources

Analytical solutions of nonlinear oscillator with coordinate-dependent mass and Euler–Lagrange equation using the parameterized homotopy perturbation method

Journal of Low Frequency Noise, Vibration and Active Control, 2019
This paper gives analytical solutions to a nonlinear oscillator with coordinate-dependent mass and Euler–Lagrange equation using the parameterized homotopy perturbation method.
MY Adamu, P Ogenyi, AG Tahir
doaj   +2 more sources

On the Euler-Lagrange equation for a variational problem

Discrete and Continuous Dynamical Systems, 2007
In this paper we prove the existence of a solution in \( L_{{\text{loc}}}^\infty \left( \Omega \right) \) to the Euler-Lagrange equation for the variational problem $$ \mathop {\inf }\limits_{\bar u + w_0^{1,\infty } \left( \Omega \right)} {\mathbf{ }}\int {_\Omega } \left( {1_D \left( {\nabla u} \right) + g\left( u \right)} \right)dx, $$ (1)
Stefano Bianchini
exaly   +2 more sources

The validity of the Euler-Lagrange equation

Discrete and Continuous Dynamical Systems, 2010
We prove the validity of the Euler-Lagrange equation for a so- lution u to the problem of minimizing R ∫,Ω(x, u(x),u(x)) dx, where L is a Carathéodory function, convex in its last variable, without assuming differen-tiability with respect to this variable.
BONFANTI, GIOVANNI, CELLINA, ARRIGO
exaly   +2 more sources

Euler-Lagrange equation for a delay variational problem

Nonautonomous Dynamical Systems, 2017
Abstract We establish Euler-Lagrange equations for a problem of Calculus of Variations where the unknown variable contains a term of delay on a ...
Joëℓ Blot
exaly   +5 more sources

Noether’s theorem for Herglotz type variational problems utilizing complex fractional derivatives [PDF]

Theoretical and Applied Mechanics, 2021
This is a review article which elaborates the results presented in [1], where the variational principle of Herglotz type with a Lagrangian that depends on fractional derivatives of both real and complex orders is formulated and the invariance of this ...
Janev Marko, Atanacković Teodor M., Pilipović Stevan   +2 more
doaj   +1 more source

Characterization and Stability of Multi-Euler-Lagrange Quadratic Functional Equations

Journal of Function Spaces, 2022
The aim of the current article is to characterize and to prove the stability of multi-Euler-Lagrange quadratic mappings. In other words, it reduces a system of equations defining the multi-Euler-Lagrange quadratic mappings to an equation, say, the multi ...
Abasalt Bodaghi, Hossein Moshtagh, Amir Mousivand   +2 more
doaj   +1 more source

Deriving the cosmological constant from the Euler–Lagrange equation of second-order differentiable gravitational field Lagrangian

AIP Advances, 2023
The principles underlying the variational approach prove to be invaluable tools in articulating physical phenomena, particularly when dealing with conserved quantities.
Ashraful Islam
doaj   +1 more source