A non-standard multiparameter eigenvalue problem in ordinary differential equations

2005 ◽  
Vol 278 (12-13) ◽  
pp. 1550-1560 ◽  
Author(s):  
M. Faierman ◽  
R. Mennicken
Keyword(s):  
Eigenvalue Problem ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Multiparameter Eigenvalue Problem

11.— A Left Definite Multiparameter Eigenvalue Problem in Ordinary Differential Equations

1976 ◽  
Vol 74 ◽  
pp. 145-155 ◽  
Author(s):  
A. Källström ◽  
B. D. Sleeman
Keyword(s):  
Eigenvalue Problem ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Ellipticity Condition ◽  
Spectral Parameters ◽  
Multiparameter Eigenvalue Problem ◽  
Sturm Liouville ◽  
Image Position

SynopsisThe main result of this paper is to establish the completeness of the eigenfunctions for the multiparameter eigenvalue problem defined by the system of ordinary differential equations0 ≤ x, ≤ 1, r = 1, …, k, subject to the Sturm-Liouville boundary conditionsr = 1, …, k. In addition it is assumed that the coefficients ars of the spectral parameters λs, satisfy the ellipticity condition , s = 1, …, k, for all xrɛ[0, 1], r = 1, …, k, and some real k-tuple μ1, …, μk and where is the co-factor of asr in the determinant . The theory developed here contrasts with the results known when …k is assumed non-vanishing for all xrɛ[0,1].

X.—The Two Parameter Sturm-Liouville Problem for Ordinary Differential Equations

1971 ◽  
Vol 69 (2) ◽  
pp. 139-148
Author(s):  
B. D. Sleeman
Keyword(s):  
Differential Equation ◽  
Eigenvalue Problem ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Liouville Problem ◽  
Sturm Liouville ◽  
Image Position ◽  
Two Parameter ◽  
General Conditions

SynopsisThis paper discusses the existence, under fairly general conditions, of solutions of the two-parameter eigenvalue problem denned by the differential equation,and three point Sturm-Liouville boundary conditions.

scholarly journals The distribution of nonprincipal eigenvalues of singular second-order linear ordinary differential equations

2006 ◽  
Vol 2006 ◽  
pp. 1-7 ◽  
Author(s):  
Juan Pablo Pinasco
Keyword(s):  
Asymptotic Behavior ◽  
Eigenvalue Problem ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Asymptotic Distribution ◽  
Counting Function ◽  
Infinite Interval ◽  
Singular Problem ◽  
Order Linear ◽  
Linear Ordinary Differential Equations

We obtain the asymptotic distribution of the nonprincipal eigenvalues associated with the singular problemx″+λq(t)x=0on an infinite interval[a,+∞). Similar to the regular eigenvalue problem on compact intervals, we can prove a Weyl-type expansion of the eigenvalue counting function, and we derive the asymptotic behavior of the eigenvalues.

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