Isoperimetric problems in the variational calculus of Euler and Lagrange
نویسندگان
چکیده
منابع مشابه
Generalized Euler–Lagrange equations for fuzzy fractional variational calculus
This paper presents the necessary optimality conditions of Euler–Lagrange type for variational problems with natural boundary conditions and problems with holonomic constraints where the fuzzy fractional derivative is described in the combined Caputo sense. The new results are illustrated by computing the extremals of two fuzzy variational problems. AMS subject classifications: 65D10, 92C45
متن کاملAn analytic study on the Euler-Lagrange equation arising in calculus of variations
The Euler-Lagrange equation plays an important role in the minimization problems of the calculus of variations. This paper employs the differential transformation method (DTM) for finding the solution of the Euler-Lagrange equation which arise from problems of calculus of variations. DTM provides an analytical solution in the form of an infinite power series with easily computable components. S...
متن کاملThe Second Euler-Lagrange Equation of Variational Calculus on Time Scales
The fundamental problem of the calculus of variations on time scales concerns the minimization of a deltaintegral over all trajectories satisfying given boundary conditions. In this paper we prove the second Euler-Lagrange necessary optimality condition for optimal trajectories of variational problems on time scales. As an example of application of the main result, we give an alternative and si...
متن کاملThe Higher Integrability and the Validity of the Euler-Lagrange Equation for Solutions to Variational Problems
We prove higher integrability properties of solutions to the problem of minimizing ∫ Ω L(x, u(x),∇u(x))dx, where ξ → L(x, u, ξ) is a convex function satisfying some additional conditions. As an application, we prove the validity of the Euler–Lagrange equation for a class of functionals with growth faster than exponential.
متن کاملan analytic study on the euler-lagrange equation arising in calculus of variations
the euler-lagrange equation plays an important role in the minimization problems of the calculus of variations. this paper employs the differential transformation method (dtm) for finding the solution of the euler-lagrange equation which arise from problems of calculus of variations. dtm provides an analytical solution in the form of an infinite power series with easily computable components. s...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Historia Mathematica
سال: 1992
ISSN: 0315-0860
DOI: 10.1016/0315-0860(92)90052-d