BOUNDARY VALUE PROBLEM FOR A THIRD-ORDER EQUATION WITH MULTIPLE CHARACTERISTICS (Innovations in Science and Technologies, 2026)
In this article the author studied one 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, for which the Green function was constructed. By solving an auxiliary problem, the original problem was reduced to a integral equation. The solvability of the integral equation was established using the contraction mapping principle.