Solvability of a Boundary Value Problem for Elliptic Differential-Operator Equations of the Second Order with a Quadratic Complex Parameter

B. A. Aliev*, V. Z. Kerimov*, Ya S. Yakubov*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)1306-1317
Number of pages12
JournalDifferential Equations
Volume56
Issue number10
DOIs
StatePublished - Oct 2020

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