TY - JOUR
T1 - Solvability of a Boundary Value Problem for Elliptic Differential-Operator Equations of the Second Order with a Quadratic Complex Parameter
AU - Aliev, B. A.
AU - Kerimov, V. Z.
AU - Yakubov, Ya S.
N1 - Publisher Copyright: © 2020, Pleiades Publishing, Ltd.
PY - 2020/10
Y1 - 2020/10
N2 - Abstract: We study the solvability of the problem for the ellipticsecond-order differential-operator equation λ2u(x)-u"(x) + Au(x) = f(x), xε(0; 1),, in a separable Hilbert space H with the boundaryconditions u'(1)+λBu(0) = f1 and u'(0) = f2, where λ is a complex parameter, A and B are given linear operators in H, the operator A is ᵩ-positive, and f, f1, and f2 are known functions. Sufficient conditions forthe unique solvability of this problem in an appropriate function space are obtained, and an upperbound (coercive if B is a bounded operator and noncoerciveif the operator B is unbounded) is established forthe solution. An application of these abstract results to elliptic boundary value problems is given.
AB - Abstract: We study the solvability of the problem for the ellipticsecond-order differential-operator equation λ2u(x)-u"(x) + Au(x) = f(x), xε(0; 1),, in a separable Hilbert space H with the boundaryconditions u'(1)+λBu(0) = f1 and u'(0) = f2, where λ is a complex parameter, A and B are given linear operators in H, the operator A is ᵩ-positive, and f, f1, and f2 are known functions. Sufficient conditions forthe unique solvability of this problem in an appropriate function space are obtained, and an upperbound (coercive if B is a bounded operator and noncoerciveif the operator B is unbounded) is established forthe solution. An application of these abstract results to elliptic boundary value problems is given.
UR - http://www.scopus.com/inward/record.url?scp=85095948959&partnerID=8YFLogxK
U2 - https://doi.org/10.1134/S00122661200100079
DO - https://doi.org/10.1134/S00122661200100079
M3 - مقالة
SN - 0012-2661
VL - 56
SP - 1306
EP - 1317
JO - Differential Equations
JF - Differential Equations
IS - 10
ER -