Results 161 to 170 of about 1,276,020 (209)

Spectral Asymptotics for Sturm-Liouville Equations

Proceedings of the London Mathematical Society, 1989
The author gives a detailed interesting survey on asymptotic formulas for various spectral characteristics of the general Sturm-Liouville problem \(-(pu')'+qu=\lambda wu\) under very mild conditions on the coefficients p,q, and w. Such spectral quantities are, for instance, the eigenvalue distribution, Green's function, the spectral function, and the ...
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Transformation of Sturm - Liouville differential equations

Functional Analysis and Its Applications, 1982
Translation from Funkts. Anal. Prilozh. 16, No.3, 42-44 (Russian) (1982; Zbl 0565.34035).
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Inverse spectral problem for the Sturm Liouville equation

Inverse Problems, 2003
Summary: This paper discusses a new numerical approach to computing the potential \(q\) in the Sturm-Liouville problem \(-y''+ qy=\lambda y\) on a compact interval. It is shown that an algorithm to recover \(q\) from eigenvalues and multiplier constants can be derived. Examples of some test problems, and questions of efficiency are discussed.
Brown, B. M., Samko, V. S., Knowles, I. W., Marletta, M.   +3 more
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Sufficient oscillation conditions for the Sturm–Liouville equation

Differential Equations, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bilal, Sh., Dzhenaliev, M. T.
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The Sturm–Liouville Equation

2006
Abstract This chapter concerns the homogeneous equation where p : [a, b] → ℝ is continuously differentiable, q : [a, b] → ℝ and ⍴: [a, b] → ℝ are continuous, p(x) > 0 and ⍴(x) > 0, for all x in [a, b], and λ is a real constant.
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The intersection of the spectra of two Sturm–Liouville equations

Applied Mathematics and Computation, 2013
This paper studies the intersection of the spectra for two Sturm-Liouville equations with general separated BCs and real coupled BCs. Under certain conditions, we proved that a two-dimensioned vectorial SLPs with separated BCs only has finitely many double eigenvalues and obtain a bound M"Q depending on Q(x) and its eigenvalues, which are larger than M"
YanXia Zhang, ZhongZhi Wang, Xuefeng Zhang   +2 more
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Variational techniques for a system of Sturm–Liouville equations

Journal of Elliptic and Parabolic Equations, 2023
The paper is concerned with the sixth order Sturm-Liouville problem \[ \begin{cases} -\left(p_i(x)u_i'''(x)\right)'''+\left(q_i(x)u_i''(x)\right)''-\left(r_i(x)u_i'(x)\right)'+s_i(x)u_i(x) =\lambda F_{u_i}(x,u_1,\dots,u_n)\\ \text{ for } 00\) and \[ \max\left\{-\frac{q_i^- T^2}{\pi^2},-\frac{q_i^- T^2}{\pi^2}-\frac{r_i^- T^4}{\pi^4},-\frac{q_i^- T^2 ...
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Preliminaries on Sturm-Liouville Equations

2020
We will consider the second-order linear ordinary differential equation $$\displaystyle -y^{\prime \prime }+q(x)y=\lambda y $$ on a finite or infinite interval. This equation is called the Sturm-Liouville equation, or often the one-dimensional Schro dinger equation .
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On the Isospectral Sixth Order Sturm-Liouville Equation

Journal of Lie Theory, 2013
A sixth-order Sturm-Liouville equation of the form \[ Ly:=-y^{(6)}+(A(z)y'')''+(B(z)y')'+C(z)y=\lambda y, \;\;\;\;a\leq z\leq b, \] is investigated with six end conditions which make a self adjoint problem. The Sturm Liouville operator is factorized as the product of a third order differential operator and its adjoint. It is shown that factorization of
Ghanbari, Kazem, Mirzaei, Hanif
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SOME PROBLEMS IN THE THEORY OF A STURM-LIOUVILLE EQUATION

Russian Mathematical Surveys, 1960
CONTENTSIntroductionChapter One. The solution of the Cauchy problem for the one dimensional wave equation § 1. The application of the method of successive approximations § 2. Reduction to the Goursat problem § 3. The solution of the mixed problem on the half line § 4. The solution of a mixed problem on a finite intervalChapter Two.
Levitan, B. M., Sargsjan, I. S.
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