In this manuscript, a numerical technique is presented for finding the eigenvalues of the regular Sturm-Liouville problems. The Chebyshev cardinal functions are used to approximate the eigenvalues of a regular Sturm-Liouville problem with Dirichlet boundary conditions. These functions defined by the Chebyshev function of the first kind. By using the operational matrix of derivative the problem ...

In this study, we suggest an efficient and useful method by using Chebyshev polynomials to approximate eigenvalues of a non-singular sixth-order Sturm-Liouville equation. This method uses Chebyshev polynomials and integration operation matrix for approximating of function and its derivatives. We convert the original problem for finding the eigenvalues of Sturm-Liouville problem to a problem of ...

In this paper, we investigate infinite product representation of the solution of a Sturm- Liouville equation with an indefinite weight function which has two zeros and/or singularities in a finite interval. First, by using of the asymptotic estimates provided in [W. Eberhard, G. Freiling, K. Wilcken-Stoeber, Indefinite eigenvalue problems with several singular points and turning points, Math. N...

We consider a singular Sturm-Liouville expression with the indefinite weight sgnx. To this expression there is naturally a self-adjoint operator in some Krein space associated. We characterize the local definitizability of this operator in a neighbourhood of ∞. Moreover, in this situation, the point ∞ is a regular critical point. We construct an operator A = (sgnx)(−d2/dx2 + q) with non-real sp...

Abstract. The Liouville tori, having an integrable metric of the form (U1(q1)− U2(q2))(dq 2 1 + dq 2 ), allow the separation of variables in the study of the Laplacian spectrum. The asymptotic analysis of the resulting Sturm-Liouville problems allows to reduce the count of the eigenvalues of the spectrum to the count of the lattice points inside a plane domain. The present paper is concerned wi...

in this paper, we investigate infinite product representation of the solution of a sturm-liouville equation with an indefinite weight function which has two zeros and/or singularitiesin a finite interval. first, by using of the asymptotic estimates provided in [w. eberhard, g.freiling, k. wilcken-stoeber, indefinite eigenvalue problems with several singular pointsand turning points, math. nachr...

for some λ ∈ C, x ∈ I = [a, b], and y ∈ C2(I). It was first introduced in a 1837 publication [7] by the eminent French mathematicians Joseph Liouville (1809 1882) and Jacques Charles François Sturm (1803 1855). At this point, our initial questions might be: why is this problem important? What can we say about the structure of this equation? How about the solutions? We will tackle a few basic re...

‎in this paper, we formulate the fourth order sturm-liouville problem (fslp) as a lie group matrix differential equation. by solving this ma- trix differential equation by lie group magnus expansion, we compute the eigenvalues of the fslp. the magnus expansion is an infinite series of multiple integrals of lie brackets. the approximation is, in fact, the truncation of magnus expansion and a gauss...

In this paper we define the Evans function for Sturm-Liouville problems. We show that the Evans function is analytic in the spectral parameter, has zeros in one-to-one correspondence with the eigenvalues, and is under certain conditions what we call conjugate symmetric. We conclude by showing that the Evans function can be used to track the movement of the eigenvalues as the coefficients in the...