Geodesic
On the Solvability of Initial Boundary-Value Problems for a Class of Operator-Differential Equations of Third Order
Matematičeskie zametki, Tome 90 (2011) no. 3, pp. 323-339

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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.
Keywords: operator-differential equation, self-adjoint operator, initial boundary-value problem, Hilbert space, Banach space, polynomial operator pencil.
Mots-clés : Fourier transform 
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     author = {A. R. Aliev},
     title = {On the {Solvability} of {Initial} {Boundary-Value} {Problems} for a {Class} of {Operator-Differential} {Equations} of {Third} {Order}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {323--339},
     publisher = {mathdoc},
     volume = {90},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2011_90_3_a0/}
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A. R. Aliev. On the Solvability of Initial Boundary-Value Problems for a Class of Operator-Differential Equations of Third Order. Matematičeskie zametki, Tome 90 (2011) no. 3, pp. 323-339. http://geodesic.mathdoc.fr/item/MZM_2011_90_3_a0/