This paper is devoted to investigating the uniform convergence conditions of Fourier series expansions continuous functions in terms eigenfunctions a Sturm-Liouville problem with eigenparameter one boundary on closed interval. Such problems are quite common mathematical physics problems.

This paper gives the analysis and numerics underlying a shooting method for approximating the eigenvalues of nonselfadjoint Sturm-Liouville problems. We consider even order problems with (equally divided) separated boundary conditions. The method can nd the eigenvalues in a rectangle and in a left half-plane. It combines the argument principle with the compound matrix method (using the Magnus e...

We present the extension of the successful Constant Perturbation Method (CPM) for Schrödinger problems to the more general class of Sturm-Liouville eigenvalue problems. Whereas the orginal CPM can only be applied to Sturm-Liouville problems after a Liouville transformation, the more general CPM presented here solves the Sturm-Liouville problem directly. This enlarges the range of applicability ...

As we know one of the most important equations which have many applications in various areas physics, mathematics, and financial markets, is Sturm–Liouville equation. In this paper, by using α-ψ-contraction technique fixed point theory employing some functional inequalities, study existence solutions partial fractional hybrid case generalized Sturm–Liouville-Langevin under boundary value condit...

We reconsider the basic formulation of second-order, two-point, Sturm-Liouville-type boundary value problems on time scales. Although this topic has received extensive attention in recent years, we present some simple examples which show that there are certain difficulties with the formulation of the problem as usually used in the literature. These difficulties can be avoided by some additional...

*Correspondence: [email protected] 1School of Mathematics, China University of Mining and Technology, Xuzhou, 221116, P.R. China Full list of author information is available at the end of the article Abstract This paper is concerned with the solvability for fractional Sturm-Liouville boundary value problems with p(t)-Laplacian operator at resonance using Mawhin’s continuation theorem. Suffic...

We examine properties of solutions to a 2n-dimensional Stieltjes Sturm-Liouville initial-value problem. Existence and uniqueness of a solution has been previously proven, but we present a proof in order to establish properties of boundedness, bounded variation, and continuity. These properties are then used to prove that the solutions depend continuously on the coefficients and on the initial c...