Inverse problems for nonlinear stationary equations

Identification of the unknown constant coefficient in the main term of the partial differential equation $-kM\psi_1(u)+g(x)\psi_2(u)=f(x)$ with the Dirichlet boundary condition is investigated. Here $\psi_i(u),\quad i=1,2,$ is a nonlinear increasing function of $u$ and $M$ is a second-order linear elliptic operator. The coefficient $k$ is recovered on the base of additional integral boundary data. The existence and uniqueness of the solution to the inverse problem with a function u and a positive real number k is proved.