On a boundary value problem for an odd-order equation with multiple characteristics

A nonlinear boundary value problem for a third-order nonlinear equation with multiple characteristics is studied in the article in a curvilinear domain. The unique solvability of the problem is proved. The uniqueness of the solution to the boundary value problem is proved by the energy integral method using some elementary inequalities. An auxiliary problem is considered for the existence of a solution, for which the Green function is constructed. By solving an auxiliary problem, the original problem is reduced to a system of Hammerstein integral equations. The solvability of a nonlinear system is proved by the contracting mapping method.