Fourth-order Birkhoff regular problems with eigenvalue parameter dependent boundary conditions

Zinsou, Bertin

doi:10.3906/mat-1509-29

Cited by 3 publications

(12 citation statements)

References 16 publications

(29 reference statements)

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“…However, they have been attracting a lot of attention. Investigations on eigenvalue parameter for dependent boundary conditions in higher order boundary value problems have seen recent developments, see for example [1][2][3]5,8,[10][11][12][14][15][16][17][18][19][20]22,23,[25][26][27].…”

Section: Introductionmentioning

confidence: 99%

“…The operators M, K and A are coefficients of powers of λ, k is the number of boundary conditions depending on λ while I is an interval. Applying separation of variables to the stability of elastic rod problems investigated in [12,14,16,17,20,[25][26][27], we get fourth order eigenvalue problems with boundary conditions depending on the eigenvalue parameter λ with the differential equation y (4) − (gy ) = λ 2 y (1.2) depending quadratically on λ.…”

Section: Introductionmentioning

confidence: 99%

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Stability of a flexible missile and asymptotics of the eigenvalues of fourth order boundary value problems

Zinsou

2023

Arab. J. Math.

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Fourth order problems with the differential equation $$y^{(4)}-(gy')'=\lambda ^2y$$ y ( 4 ) - ( g y ′ ) ′ = λ 2 y , where $$g\in C^1[0,a]$$ g ∈ C 1 [ 0 , a ] and $$a>0$$ a > 0 , occur in engineering on stability of elastic rods. They occur as well in aeronautics to describe the stability of a flexible missile. Fourth order Birkhoff regular problems with the differential equation $$y^{(4)}-(gy')'=\lambda ^2y$$ y ( 4 ) - ( g y ′ ) ′ = λ 2 y and eigenvalue dependent boundary conditions are considered. These problems have quadratic operator representations with non-self-adjoint operators. The first four terms of the asymptotics of the eigenvalues of the problems as well as those of the eigenvalues of the problem describing the stability of a flexible missile are evaluated explicitly.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stability of a flexible missile and asymptotics of the eigenvalues of fourth order boundary value problems

Zinsou

2023

Arab. J. Math.

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“…Such problems are realized as operator polynomials, also called operator pencils. Some recent developments of higher order differential operators whose boundary conditions may depend on the eigenvalue parameter have been investigated in [5,6,8,9,10,11,13,14,15].…”

Section: Introductionmentioning

confidence: 99%

“…Separation of variables leads the stability of elastic rod problems investigated in [5,6,8,9,14,15] to fourth order eigenvalue problems with eigenvalue parameter dependent boundary conditions, where the differential equation…”

Section: Introductionmentioning

confidence: 99%

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Stability of a flexible missile described by asymptotics of the eigenvalues of fourth order boundary value problems

Zinsou

2021

Preprint

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Fourth order problems, with the differential equation y (4) − (gy ′ ) ′ = λ 2 y, where g ∈ C 1 [0, a] and a > 0, occur in engineering on stability of elastic rods. They occur as well in aeronautics to describe the stability of a flexible missile. Fourth order Birkhoff regular problems with the differential equation y (4) − (gy ′ ) ′ = λ 2 y and eigenvalue dependent boundary conditions are considered. These problems have quadratic operator representations with non self-adjoint operators. The first four terms of the asymptotics of the eigenvalues of the problems as well as those of the eigenvalues of the problem describing the stability of a flexible missile are evaluated explicitly.

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Stability of a flexible missile and asymptotics of the eigenvalues of fourth order boundary value problems

Zinsou

2024

Preprint

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Fourth order problems with the differential equation $y^{(4)}-(gy’)’=\lambda^2y$, where $g\in C^1[0,a]$ and $a>0$, occur in engineering on stability of elastic rods. They occur as well in aeronautics to describe the stability of a flexible missile. Fourth order Birkhoff regular problems with the differential equation $y^{(4)}-(gy’)’=\lambda^2y$ and eigenvalue dependent boundary conditions are considered. These problems have quadratic operator representations with non self-adjoint operators. The first four terms of the asymptotics of the eigenvalues of the problems as well as those of the eigenvalues of the problem describing the stability of a flexible missile are evaluated explicitly.

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Fourth-order Birkhoff regular problems with eigenvalue parameter dependent boundary conditions

Abstract: A regular fourth-order differential equation that depends quadratically on the eigenvalue parameter λ is considered with classes of separable boundary conditions independent of λ or depending on λ linearly. Conditions are given for the problems to be Birkhoff regular.

Cited by 3 publications

References 16 publications

Stability of a flexible missile and asymptotics of the eigenvalues of fourth order boundary value problems

Stability of a flexible missile and asymptotics of the eigenvalues of fourth order boundary value problems

Stability of a flexible missile described by asymptotics of the eigenvalues of fourth order boundary value problems

Stability of a flexible missile and asymptotics of the eigenvalues of fourth order boundary value problems

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