In this paper we have chosen to work with two different approaches solving the inverse problem of calculus variation. The first approach is based on an integral representation Lagrangian function that uses equation motion while second one relies a generalization well known Noether's theorem and constructs directly from motion. As application provide some useful remarks for modified Emden-type t...

Abstract In the present work, firstly, we use a minimax equality to prove existence of solution certain system varitional equations providing numerical approximation such solution. Then, propose method solve collage-type inverse problem associated with corresponding system, and illustrate behaviour example.

A 3D slip-dependent frictional contact problem in elastostatics is discussed. We deliver a variational formulation as a mixed variational problem whose Lagrange multipliers set is solutiondependent. Then, the existence and the boundedness of the solutions is investigated. The proof is based on a recent result for an abstract mixed variational problem with solution-dependent set of Lagrange mult...