Half-linear Sturm–Liouville Problem with Weights: Asymptotic Behavior of Eigenfunctions

2014 ◽  
Vol 284 (01) ◽  
pp. 157-162
Author(s):  
Pavel Drábek ◽  
Alois Kufner ◽  
Komil Kuliev
Keyword(s):  
Asymptotic Behavior ◽  
Liouville Problem ◽  
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.

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).

Sturm-Liouville Problem for Stationary Differential Operator with Nonlocal Two-Point Boundary Conditions

2006 ◽  
Vol 11 (1) ◽  
pp. 47-78 ◽  
Author(s):  
S. Pečiulytė ◽  
A. Štikonas
Keyword(s):  
Boundary Condition ◽  
Differential Operator ◽  
Boundary Conditions ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Liouville Problem ◽  
Complex Case ◽  
Qualitative Behavior ◽  
Point Boundary ◽  
Sturm Liouville

The Sturm-Liouville problem with various types of two-point boundary conditions is considered in this paper. In the first part of the paper, we investigate the Sturm-Liouville problem in three cases of nonlocal two-point boundary conditions. We prove general properties of the eigenfunctions and eigenvalues for such a problem in the complex case. In the second part, we investigate the case of real eigenvalues. It is analyzed how the spectrum of these problems depends on the boundary condition parameters. Qualitative behavior of all eigenvalues subject to the nonlocal boundary condition parameters is described.

scholarly journals On partial fractional Sturm–Liouville equation and inclusion

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Zohreh Zeinalabedini Charandabi ◽  
Hakimeh Mohammadi ◽  
Shahram Rezapour ◽  
Hashem Parvaneh Masiha
Keyword(s):  
Differential Equation ◽  
Liouville Equation ◽  
Existence Of Solutions ◽  
Liouville Problem ◽  
Existence Of A Solution ◽  
Contractive Mappings ◽  
Sturm Liouville

AbstractThe Sturm–Liouville differential equation is one of interesting problems which has been studied by researchers during recent decades. We study the existence of a solution for partial fractional Sturm–Liouville equation by using the α-ψ-contractive mappings. Also, we give an illustrative example. By using the α-ψ-multifunctions, we prove the existence of solutions for inclusion version of the partial fractional Sturm–Liouville problem. Finally by providing another example and some figures, we try to illustrate the related inclusion result.

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