Solution dependence on problem parameters for initial-value problems associated with the Stieltjes Sturm-Liouville equations

Date

2005-01-02

Authors

Battle, Laurie

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University-San Marcos, Department of Mathematics

Abstract

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 conditions under certain hypotheses. In a future paper, these results will be extended to eigenvalue problems, and we will examine dependence on the endpoints and boundary data in addition to the coefficients. We will find conditions under which the eigenvalues depend continuously and differentiably on these parameters.

Description

Keywords

Initial value problems, Continuous dependence, Linear systems

Citation

Battle, L. (2005). Solution dependence on problem parameters for initial-value problems associated with the Stieltjes Sturm-Liouville equations. <i>Electronic Journal of Differential Equations, 2005</i>(02), pp. 1-18.

Rights

Attribution 4.0 International

Rights Holder

Rights License