A STUDY OF NONLOCAL NONLINEAR BOUNDARY VALUE PROBLEMS FOR THIRD-ORDER EQUATIONS WITH MULTIPLE CHARACTERISTICS

<p>In this article, the authors studied one nonlcal nonlinear boundary value problem for a third-order nonlinear equation with multiple characteristics. The unique solvability to the problem was proven. The uniqueness of the solution to the boundary value problem was proven by the method of energy. To prove the existence of a solution to this problem, an auxiliary problem was considered. The solution of an auxiliary problem reduced the original problem to a nonlinear integral equation. Subsequently, the solvability of the nonlinear integral equation was established.</p>