Mixed problem for a nonlinear differential equation of the seventh order with identification source

In this paper, a seventh order nonlinear partial differential equations with mixed and additional conditions and positive parameter is considered. The Fourier spectral method of separation of variables is applied. Countable systems of nonlinear functional-integral equations are derived. Theorem on the uniqueness and existence of the solution of inverse problem is proved for some values of parameter. The method of contraction mapping in Banach space is applied. The solution of the inverse problem is obtained in the form of Fourier series. Theorem on absolute and uniform convergence of Fourier series is proved.