On the solvability of initial boundary-value problems for a class of operator-differential equations of third order

被引：0
作者：
A. R. Aliev
机构：
[1] Baku State University,Institute of Mathematics and Mechanics
来源：
Mathematical Notes | 2011年 / 90卷
关键词：
operator-differential equation; self-adjoint operator; initial boundary-value problem; Hilbert space; Banach space; Fourier transform; polynomial operator pencil;
D O I：
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摘要：
We obtain sufficient conditions for the regular solvability of initial boundary-value problems for a class of operator-differential equations of third order with variable coefficients on the semiaxis. These conditions are expressed only in terms of the operator coefficients of the equations under study. We obtain estimates of the norms of intermediate derivative operators via the discontinuous principal parts of the equations and also find relations between these estimates and the conditions for regular solvability.
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[1]  
Agmon S.(1963)Properties of solutions of ordinary differential equations in Banach space Comm. Pure Appl. Math. 16 121-239
[2]  
Nirenberg L.(1971)On the theory of polynomial operator pencils Dokl. Akad. Nauk SSSR 199 747-750
[3]  
Gasymov M. G.(1971)The multiple completeness of part of the eigen-and associated vectors of polynomial operator pencils Izv. Akad. Nauk Armyan. SSR Ser. Mat. 6 131-147
[4]  
Gasymov M. G.(1983)Self-adjoint quadratic operator pencils and elliptic problems Funktsional. Anal. Prilozhen. 17 38-61
[5]  
Kostyuchenko A. G.(1983)Multiple completeness of root vectors of polynomial operator pencils corresponding to Funktsional. Anal. Prilozhen. 17 84-85
[6]  
Shkalikov A. A.(1983) problems on the semiaxis Dokl. Akad. Nauk SSSR 273 292-295
[7]  
Mirzoev S. S.(1988)Conditions for the correct solvability of boundary-value problems for operator-differential equations Mat. Sb. 135 96-118
[8]  
Mirzoev S. S.(1989)Strongly damped pencils of operators and solvability of the corresponding operator-differential equations Tr. Semin. Im. I.G. Petrovskogo 14 140-224
[9]  
Shkalikov A. A.(1992)Elliptic equations in Hilbert space and spectral problems connected with them Differ. Uravn. 28 651-661
[10]  
Shkalikov A. A.(2003)Solvability of boundary-value problems for second-order operator-differential equations of elliptic type Mat. Sb. 194 3-12
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