Variational method for the solution of an inverse problem

This paper presents a variational method for the solution of an inverse problem. An inverse problem of determining the unknown coefficient of nonlinear time-dependent Schrödinger equation is considered. Inverse problem is reformulated as a variational problem by means of an observation functional. The existence and uniqueness of solutions of the constituted variational problem are investigated. The differentiability of observation functional is obtained and a necessary condition for the solution of the variational problem is given.