Results 171 to 180 of about 1,276,020 (209)

The Periodic Sturm–Liouville Equations

2017
We begin with a brief introduction the periodic Sturm–Liouville equations \([p(x)y'(x)]' + [\lambda w(x) - q(x)] y(x) = 0\). After reviewing some elementary knowledge of the theory of a general class of second-order linear homogeneous ordinary differential equations, we introduce two basic Sturm theorems on the zeros of solutions of the equations. Then,
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A Coupled System of Sturm–Liouville Differential Equations

Mathematical Notes
In this paper, the authors investigate the existence and the asymptotic behavior of positive continuous solutions of the following nonlinear coupled system: \[ \left\{ \begin{array}{c} -\frac{1}{A}(Au')'=a(x)u^pv^r \quad \text{on}\ (0,1)\\ -\frac{1}{B}(Bu')'=b(x)u^qv^s\quad \text{on}\ (0,1),\\ u(0)=u(1)=v(0)=v(1)=0, \end{array} \right. \] where \(p, q \
Belkahla, S., ZineElAbidine, Z.
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Sharp bounds of nodes for Sturm–Liouville equations

Monatshefte für Mathematik
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Hao Feng, Gang Meng, Ping Yan, Lijuan Zhou   +3 more
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Stability of solutions to Sturm-Liouville diffusion equations

Transport Theory and Statistical Physics, 1986
Abstract Stability of solutions of abstract half-space problems of the type T ψ'1 (x)=-Aψ(x)(0> x > ∞) is established under perturbations of the resolvent of the (unbounded) positive self-adjoint operator A. Applications are given to Sturm-Liouville type diffusion equations.
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Inverse problem for Sturm-Liouville and hill equations

Annali di Matematica Pura ed Applicata, 1987
We discuss the inverse Sturm-Liouville problem on a finite interval by the method of transformation kernel. The \(\tau\)-function, the Fredholm determinant of the transformation kernel, is explicitly written down in terms of the spectral data, from which a very explicit representation formula for the potential is deduced, and well-posedness of the ...
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DISTRIBUTION OF THE EIGENVALUES OF THE STURM-LIOUVILLE OPERATOR EQUATION

Mathematics of the USSR-Izvestiya, 1977
This work contains an analysis of the dependence of the lower terms of the asymptotics of the distribution of the eigenvalues of the equation upon the spectrum of the positive selfadjoint operator and the form of the boundary conditions. As a corollary the second term is found for the spectral asymptotics of classical boundary value problems for the ...
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Inverse Problem for the Sturm--Liouville Equation on a Simple Graph

SIAM Journal on Mathematical Analysis, 2000
A Sturm-Liouville problem on a graph of three joint strings with the free ends fixed is considered. The direct problem of the location of the spectrum and the inverse problem of recovering the potential from the spectrum are studied. First, an auxiliary problem with two strings is investigated, which leads to a quadratic operator pencil, and properties
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A Catalogue of Sturm-Liouville Differential Equations

2005
This catalogue commences with sections devoted to a brief summary of Sturm-Liouville theory including some details of differential expressions and equations, Hilbert function spaces, differential operators, classification of interval endpoints, boundary condition functions and the Liouville transform.
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The Sturm—Liouville equation II

2022
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On a Partial Fractional Hybrid Version of Generalized Sturm–Liouville–Langevin Equation

Fractal and Fractional, 2022
Javad Izadi, Reny George, Shahram Rezapour   +2 more
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