2016
DOI: 10.3906/mat-1509-29
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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.

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Cited by 3 publications
(12 citation 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%
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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%
“…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%
See 1 more Smart Citation