A projection method for a third-order operator differential equation with a nonlinear monotone operator

We study the Galerkin method for a third-order operator-differential equation with the main self-adjoint operator $A$ and the subordinate nonlinear monotone operator $K$ in a separable Hilbert space. The existence and uniqueness of a strong solution to the original problem are proved. Convergence estimates for the Galerkin method are obtained.