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L. Goddard (1962)
Linear Differential OperatorsNature, 195
M. Moller, A. Zettl (1995)
Semi-boundedness of Ordinary Differential OperatorsJournal of Differential Equations, 115
M. Gimadislamov (2005)
On the spectrum of a differential operator of high-orderMathematical Notes, 77
P. Binding, P. Browne, B. Watson (2002)
STURM–LIOUVILLE PROBLEMS WITH BOUNDARY CONDITIONS RATIONALLY DEPENDENT ON THE EIGENPARAMETER. I, 45
R. Douglas (1972)
Banach Algebra Techniques in Operator Theory
M. Marletta, A. Shkalikov, C. Tretter (2003)
Pencils of differential operators containing the eigenvalue parameter in the boundary conditionsProceedings of the Royal Society of Edinburgh: Section A Mathematics, 133
Xiaoling Hao, Jiong Sun, Aiping Wang, A. Zettl (2009)
Characterization of Domains of Self-Adjoint Ordinary Differential Operators IIResults in Mathematics, 61
G. Bonanno, B. Bella (2008)
A boundary value problem for fourth-order elastic beam equationsJournal of Mathematical Analysis and Applications, 343
E. Kir, Gülen Başcanbaz-Tunca, C. Yanik (2005)
SPECTRAL PROPERTIES OF A NON SELFADJOINT SYSTEM OF DIFFERENTIAL EQUATIONS WITH A SPECTRAL PARAMETER IN THE BOUNDARY CONDITIONProyecciones (antofagasta), 24
A. Shkalikov (1986)
Boundary problems for ordinary differential equations with parameter in the boundary conditionsJournal of Soviet Mathematics, 33
A. Zettl (1975)
Formally self-adjoint quasi-differential operatorsRocky Mountain Journal of Mathematics, 5
J. Weidmann (1987)
Spectral Theory of Ordinary Differential Operators
N. Kerimov, Z. Aliev (2007)
The basis properties of eigenfunctions in the eigenvalue problem with a spectral parameter in the boundary conditionDoklady Mathematics, 75
Friedrich Sauvigny (2012)
Linear Operators in Hilbert Spaces
M. Moller, A. Zettl (1995)
Symmetrical Differential Operators and Their Friedrichs ExtensionJournal of Differential Equations, 115
M. Möller, V. Pivovarchik (2006)
Spectral Properties of a Fourth Order Differential EquationZeitschrift Fur Analysis Und Ihre Anwendungen, 25
N. Kerimov, Z. Aliev (2007)
On the basis property of the system of eigenfunctions of a spectral problem with spectral parameter in the boundary conditionDifferential Equations, 43
) is self-adjoint if and only if #({0, 3} ∩ P 0 ) ≤ 1, #({1, 2} ∩ P 0 ) ≤ 1, #({0, 3} ∩ P a ) ≤ 1 and #({1
Aiping Wang, Jiong Sun, A. Zettl (2008)
The classification of self-adjoint boundary conditions: Separated, coupled, and mixedJournal of Functional Analysis, 255
V. Pivovarchik, C. Mee (2001)
The inverse generalized Regge problemInverse Problems, 17
M. Möller, A. Zettl (1993)
Weighted norm inequalities for the quasi-derivatives of ordinary differential operatorsResults in Mathematics, 24
H. Behncke (2006)
Spectral analysis of fourth order differential operators IMathematische Nachrichten, 279
D. Hinton (1979)
AN EXPANSION THEOREM FOR AN EIGENVALUE PROBLEM WITH EIGENVALUE PARAMETER IN THE BOUNDARY CONDITIONQuarterly Journal of Mathematics, 30
H. Frentzen (1982)
Equivalence, adjoints and symmetry of quasi-differential expressions with matrix-valued coefficients and polynomials in themProceedings of the Royal Society of Edinburgh: Section A Mathematics, 92
Tosio Kato (1966)
Perturbation theory for linear operators
3} ∩ P 0 ) = 0, #({1, 2} ∩ P 0 ) = 0, #({0, 3} ∩ P a ) = 0 and #({1, 2} ∩ P a ) = 0 and the differential operator T (U ) is self-adjoint
N. Kerimov, Z. Aliev (2007)
On the basis property of the system of eigenfunctions of a spectral problem with a spectral parameter in the boundary condition (Russian)
R. Mennicken, M. Möller (2003)
Non-Self-Adjoint Boundary Eigenvalue Problems
We consider the eigenvalue problem y (4)(λ,x) − (gy′)′(λ,x) = λ 2 y(λ,x) with separated boundary conditions B j (λ)y = 0 for j = 1,…,4, where g ∈ C 1[0, a] is a real valued function, B j (λ)y = y [p j ](a j ) or B j (λ)y = y [pj](a j ) + iϵ j αλy [qj ] (aj ), aj = 0 for j = 1, 2 and a j = a for j = 3, 4, α > 0, ϵ j ∈ {−1, 1}. We will associate to the above eigenvalue problem a quadratic operator pencil L(λ) = λ 2 M − iαλK − A in the space , where and are bounded self-adjoint operators and k is the number of boundary conditions which depend on λ. We give necessary and sufficient conditions for the operator A to be self-adjoint.
Quaestiones Mathematicae – Taylor & Francis
Published: Sep 1, 2011
Keywords: Primary: 34B07; Secondary: 34L99; 47E05; Fourth order differential equation; eigenvalue dependent boundary conditions; quadratic operator pencil; self-adjoint operator
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