A general backwards calculus of variations via duality

作者：Malinowska Agnieszka B; Torres Delfim F M^*

来源：Optimization Letters, 2011, 5(4): 587-599.

DOI：10.1007/s11590-010-0222-x

• Calculus of variations
• Composition of functionals
• Euler-Lagrange equations
• Natural boundary conditions
• Time scales
• Duality

We prove Euler-Lagrange and natural boundary necessary optimality conditions for problems of the calculus of variations which are given by a composition of nabla integrals on an arbitrary time scale. As an application, we get optimality conditions for the product and the quotient of nabla variational functionals.

• 出版日期2011-11