Asymptotic Behavior for Eigenvalues of the Singular Sturm-Liouville Problem with Transmission Conditions

2020 ◽  
Author(s):  
Dan Mu ◽  
Ji-jun Ao
Keyword(s):  
Asymptotic Behavior ◽  
Liouville Problem ◽  
Transmission Conditions ◽  
Sturm Liouville

scholarly journals Spectral deformation in a problem of singular perturbation theory

2019 ◽  
Vol 484 (4) ◽  
pp. 397-400
Author(s):  
S. A. Stepin ◽  
V. V. Fufaev
Keyword(s):  
Perturbation Theory ◽  
Asymptotic Behavior ◽  
Integral Method ◽  
Deformation Parameter ◽  
Liouville Problem ◽  
Singular Perturbation Theory ◽  
Different Types ◽  
Spectral Deformation ◽  
Sturm Liouville ◽  
Spectral Complex

Quasi-classical asymptotic behavior of the spectrum of a non-self-adjoint Sturm–Liouville problem is studied in the case of a one-parameter family of potentials being third-degree polynomials. For this problem, the phase-integral method is used to derive quantization conditions characterizing the asymptotic distribution of the eigenvalues and their concentration near edges of the limit spectral complex. Topologically different types of limit configurations are described, and critical values of the deformation parameter corresponding to type changes are specified.

scholarly journals The Parseval identity for q-Sturm–Liouville problems with transmission conditions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nida Palamut Koşar
Keyword(s):  
Liouville Problem ◽  
Transmission Conditions ◽  
Spectral Functions ◽  
Expansion Formula ◽  
Sturm Liouville

AbstractIn the present study, we investigate the existence of spectral functions and obtain the Parseval identity and expansion formula in eigenfunctions for the singular q-Sturm–Liouville problem with transmission conditions.

Multiparameter Variational Eigenvalue Problems With Indefinite Nonlinearity

1997 ◽  
Vol 49 (5) ◽  
pp. 1066-1088 ◽  
Author(s):  
Tetsutaro Shibata
Keyword(s):  
Asymptotic Behavior ◽  
Asymptotic Formula ◽  
Optimal Condition ◽  
Level Set ◽  
Eigenvalue Problems ◽  
Liouville Problem ◽  
General Level ◽  
Sturm Liouville ◽  
Image Position

AbstractWe consider the multiparameter nonlinear Sturm-Liouville problemwhere are parameters. We assume that1 ≤ q ≤ p1 < p2 < ... ≤ pn < 2q + 3.We shall establish an asymptotic formula of variational eigenvalue λ = λ(μ, α) obtained by using Ljusternik-Schnirelman theory on general level set Nμ, α(α < 0 : parameter of level set). Furthermore,we shall give the optimal condition of {(μ, α)}, under which μi(m + 1 ≤ i ≤ n : fixed) dominates the asymptotic behavior of λ(μ, α).

Sign in / Sign up

Export Citation Format

Share Document