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 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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- 1.Gorbachuk, V.I. and Rybak, M.A., On boundary-value problems for Sturm–Lioville equation with a spectral parameter in the equation and in a boundary condition, in Direct and Inverse Problems of Scattering Theory, Kiev, 1981, pp. 3–16.Google Scholar
- 4.Aliev, B.A., Asymptotic behavior of eigenvalues of a boundary value problem with spectral parameter in the boundary conditions for the second-order elliptic differential-operator equation, Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci., 2005, vol. 25, no. 7, pp. 3–8.MathSciNetGoogle Scholar
- 12.Yakubov, Ya., Elliptic differential-operator problems with the spectral parameter in both the equation and boundary conditions and the corresponding abstract parabolic initial boundary value problems, in New Prospects in Direct, Inverse and Control Problems for Evolution Equations, Springer INdAM Series, 2014, vol. 10, pp. 437–471.MathSciNetMATHGoogle Scholar
- 18.Krein, S.G., Lineinye differentsial’nye uravneniya v Banakhovom prostranstve (Linear Differential Equations in Banach space), Moscow: Nauka, 1967.Google Scholar
- 20.Krein, S.G., Lineinye uravneniya v Banakhovom prostranstve (Linear Equations in Banach space), Moscow: Nauka, 1971.Google Scholar