Eigenvalue and Eigenfunction Asymptotics for Regular Sturm-Liouville Problems

Fulton, Charles T.; Pruess, Steven

doi:10.1006/jmaa.1994.1429

Cited by 95 publications

(65 citation statements)

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“…Except for some minor notational changes, and the rearrangement of some terms which do not commute in the vector case, our estimates and their proofs are very similar to those appearing in [4]. The reader may consult this reference for the proofs of Lemma 2.1 and Lemma 2.2.…”

Section: Preliminary Resultssupporting

confidence: 49%

Compactness of Floquet isospectral sets for the matrix Hill's equation

Carlson

2000

Proc. Amer. Math. Soc.

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Section: Preliminary Resultssupporting

confidence: 49%

Compactness of Floquet isospectral sets for the matrix Hill's equation

Carlson

2000

Proc. Amer. Math. Soc.

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“…If we take (x) 0 and/or 1 = 2 = 1 and/or a(x) 1 then the asymptotic formulas for eigenvalues and eigenfunctions correspond to those for the classical Sturm-Liouville problem [10,14,[16][17][18].…”

Section: Erdo ¼ Ganşen and Azad Bayram Ovmentioning

confidence: 99%

Spectral analysis of boundary value problems with retarded argument

BAYRAMOV¹

2017

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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Abstract. In this paper, by modifying some techniques of [S.B. Norkin, Differential equations of the second order with retarded argument, Translations of Mathematical Monographs, Vol. 31, AMS, Providence, RI, 1972] and suggesting own approaches we …nd asymptotic formulas for the eigenvalues and eigenfunctions of boundary value problems of Sturm-Liouville type for the second order di¤erential equation with retarded argument. Formulation of the problemIn this study we shall investigate discontinuous eigenvalue problems which consist of Sturm-Liouville equation; with boundary conditionsand transmission conditionswhere a(x) = a 2 1 for x 2 0; 2 and a(x) = a 2 2 for x 2 2 ; ; the real-valued function M (x) is continuous in 0; 2 [ 2 ;and has a …nite limit M ( 2 0) = lim x! 2 0 M (x); the real valued function (x) 0 continuous in 0; 2 [ 2 ; and has a …nite limit ( 2 0) = lim x! 2 0 (x), x (x) 0; if x 2 0; 2 ; x (x)

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“…The approach used in [2] is based on an iterative procedure solving the associated Riccati equation and producing an asymptotic expansion of the solution in the higher powers of 1/2 1 / λ as λ → ∞ for smooth ( ) q t . There is also a vast amount of literature dealing with asymptotic estimates of eigenvalues for standard Sturm-Liouville problems with regular endpoints [3,4,5,6,9,10,11,13,14]. Here we follow the similar approach in [4,10,12].…”

Section: Introductionmentioning

confidence: 99%