## Abstract

Problems are formulated for abstract higher-order elliptic equations on the semiaxis and on a finite interval and general theorems for the Fredholm solvability and exact solvability of these equations given emission conditions to infinity are proved. A classification of the real spectrum of the pencil associated with the equation is presented, and possible rules for rigorous selection of the segment of its eigenelements and associated elements formulated. Completeness, minimality, and the basis property of the fundamental solutions of the equation in the solution space, along with the properties of the derivative chains of the eigenelements and associated elements of the pencil that correspond to problems on the semiaxis and on a finite interval are studied.

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Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 14, pp. 140–224, 1989.

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Shkalikov, A.A. Elliptic equations in hilbert space and associated spectral problems.
*J Math Sci* **51**, 2399–2467 (1990). https://doi.org/10.1007/BF01097162

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DOI: https://doi.org/10.1007/BF01097162