ON A BOUNDARY VALUE PROBLEM FOR AN ODD-ORDER EQUATION WTH MULTIPLE CHARACTERISTICS
Keywords:
nonlinearity, uniqueness, existence, system of Hammerstein equations.Abstract
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. By solving an auxiliary problem, the original problem was reduced to a system of Hammerstein integral equations.The solvability of a nonlinear system is established by the method of contraction mappings.
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