Abstract
In this paper, we obtain sufficient conditions for the existence of a unique regular solution of the boundary-value problems for operator differential equations of order 2k with variable coefficients. These conditions are expressed solely in terms of operator coefficients of the equations under study.
Similar content being viewed by others
REFERENCES
J.-L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications, Dunod, Paris, 1968; Russian translation: Mir, Moscow, 1971.
S. Agmon and L. Nirenberg, “Properties of solutions of ordinary differential equations in Banach space, ” Comm. Pure Appl. Math., 16 (1963), 121–239.
M. G. Gasymov, “On the theory of polynomial operator bundles, ” Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.], 199 (1971), no. 4, 747–750.
M. G. Gasymov, “On multiple completeness of part of the eigen and adjoint vectors of polynomial operator bundles, ” Izv. Akad. Armyan. SSR Ser. Mat., 6 (1971), no. 2–3, 131–147.
S. S. Mirzoev, “On multiple completeness of the root vectors of polynomial operator bundles corresponding to boundary-value problems on the semiaxis” Funktsional. Anal. i Prilozhen. [Functional Anal. Appl.], 17 (1983), no. 2, 84–85.
S. S. Mirzoev, “Conditions for the well-defined solvability of boundary-value problems for operator differential equations, ” Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.], 273 (1983), no. 2, 292–295.
Yu. A. Dubinskii, “On operator differential equations of arbitrary order” Mat. Sb. [Russian Acad. Sci. Sb. Math.], 90 (132), no. 1, 3–22.
A. A. Shkalikov, “Elliptic equations in Hilbert space and spectral problems related to them” Trudy Sem. Petrovsk. (1989), no. 14, 140–224.
S. S. Mirzoev, Questions of the Theory of Solvability of Boundary-Value Problems for Operator Differential Equations in Hilbert Space and Spectral Problems Related to Them [in Russian], Doctoral (Phys.–Math.) Dissertation, Baku State Univ., Baku, 1994.
S. Ya. Yakubov, Linear Operator Differential Equations and Their Applications [in Russian], ÉLM, Baku, 1985.
O. A. Oleinik, “Boundary-value problems for linear equations of elliptic and parabolic type with discontinuous coefficients, ” Izv. Akad. Nauk SSSR Ser. Mat. [Math. USSR-Izv.], 25 (1961), nos. 1–3, 3–20.
I. V. Girsanov, “On the solution of boundary-value problems for parabolic and elliptic equations with discontinuous coefficients” Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.], 135 (1960), no. 6, 1311–1313.
S. S. Mirzoev and A. R. Aliev, “On a boundary-value problem for operator differential equations of second order with discontinuous coefficient, ” Trudy Inst. Matem. Mekh. Acad. Nauk Azerbaidzhan, 7 (15) (1997), 18–25.
A. R. Aliev, On the Well-Defined Solvability of Boundary-Value Problems for Operator Differential Equations with Discontinuous Coefficients [in Russian], Cand. Sci. (Phys.–Math.) Dissertation, Baku State Univ., Baku, 1998.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Aliev, A.R. Boundary-Value Problems for a Class of Operator Differential Equations of High Order with Variable Coefficients. Mathematical Notes 74, 761–771 (2003). https://doi.org/10.1023/B:MATN.0000009012.36858.86
Issue Date:
DOI: https://doi.org/10.1023/B:MATN.0000009012.36858.86