(untitled) (Texas Journal of Multidisciplinary Studies, 2022)
For nonlinear equations, the Kattabrig problem has been used in some boundary value problems for third-order equations. Such equations are called multiple equations. For equations of the third order multiple characteristics in a finite field, the problem of a nonlinear equation in a boundary value problem is posed and the Green function is constructed for this problem, and the existence and uniqueness of the solution of the problem is indicated. It is also important to show the existence and uniqueness of the solution of boundary value problems in infinite fields for the equation of the third order multiple characteristics.