On a Boundary Value Problem for Operator-Differential Equations in Hilbert Space

In this paper, we study regular and Fredholm solvability of a Neumann type boundary value problem for a second order elliptic type equation with operator coefficients for a separable Hilbert space on a finite domain.The conditions of regular and Fredholm solvability for the given problem in terms of only the coefficients of the equation are found.The estimates for intermediate derivatives operators are obtained.These estimates determine the solvability conditions for our problem.Note that the considered operator equations have variable coefficients.

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