# Article

**Keywords:**

identification problem; nonlinear Gao beam; Wirtinger's inequality; Wirtinger-Poincaré-Almansi inequality

**Summary:**

Identification problem is a framework of mathematical problems dealing with the search for optimal values of the unknown coefficients of the considered model. Using experimentally measured data, the aim of this work is to determine the coefficients of the given differential equation. This paper deals with the extension of the continuous dependence results for the Gao beam identification problem with different types of boundary conditions by using appropriate analytical inequalities with a special attention given to the Wirtinger's inequality and its modification. On the basis of these results for the different types of the boundary conditions the existence theorem for the identification problem can be proven.