Boundary Value Problem for an Odd Order Equation with Multiple Characteristics

We prove the unique solvability of the nonlinear boundary value problem for an odd order nonlinear equation with multiple characteristics in a curvilinear domain. The uniqueness of a solution is established by the method of energy integrals by using some elementary inequalities and Friedrichs type inequalities. To prove the existence of a solution to this problem, an auxiliary problem is considered whose Green function is constructed. With the help of this auxiliary problem, the original problem is reduced to a system of Hammerstein integral equations. The solvability of the nonlinear system is proved by the contraction mapping principle.