Optimal control problem with controls in coefficients of quasilinear elliptic equation

The optimal control problem with controlling functions in coecients of multidi-mensional quasilinear elliptic type equation is considered. Studding optimal control problem consist the nonlinear phase and integral constraints and nonlinear quality criterion in general integral form. Correctness of this problem is investigated, existence theorem are proved and the necessary condition in the form of the generalized rule of Lagrange multipliers for optimality of solution is established. Found the formula for variation of quality criterion, which may be used in numerical treatments.