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2018•Differential EquationsRequires access

Solvability of a Boundary Value Problem for Second-Order Elliptic Differential Operator Equations with a Spectral Parameter in the Equation and in the Boundary Conditions

B. A. Aliev, N. K. Kurbanova, Ya. Yakubov

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Abstract

In a Hilbert space H , we study noncoercive solvability of a boundary value problem for second-order elliptic differential-operator equations with a spectral parameter in the equation and in the boundary conditions in the case where the leading part of one of the boundary conditions contains a bounded linear operator in addition to the spectral parameter. We also illustrate applications of the general results obtained to elliptic boundary value problems.

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What this paper is about

In a Hilbert space H , we study noncoercive solvability of a boundary value problem for second-order elliptic differential-operator equations with a spectral parameter in the equation and in the boundary conditions in the case where the leading part of one of the boundary conditions contains a bounded linear operator in addition to the spectral parameter. We also illustrate applications of the general results obtained to elliptic boundary value problems.

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OpenAlex reports 3 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In a Hilbert space H , we study noncoercive solvability of a boundary value problem for second-order elliptic differential-operator equations with a spectral parameter in the equation and in the boundary conditions in the case where the leading part of one of the boundary conditions contains a bounded linear operator in addition to the spectral parameter. We also illustrate applications of the general results obtained to elliptic boundary value problems.

Key concepts: Mathematics, Boundary value problem, Poincaré–Steklov operator, Mathematical analysis, Elliptic operator, Semi-elliptic operator, Free boundary problem, Elliptic boundary value problem

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Solvability of a Boundary Value Problem for Second-Order Elliptic Differential Operator Equations with a Spectral Parameter in the Equation and in the Boundary Conditions — Research Paper | ScholarLens