Electron. J. Diff. Eqns., Vol. 2005(2005), No. 02, pp. 1-18.

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

Laurie Battle

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.

Submitted September 10, 2004. Published January 2,2005.
Math Subject Classifications: 34A12, 34A30.
Key Words: Initial value problems; continuous dependence; linear systems.

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Laurie Battle
Department of Mathematics and Computer Science
Campus Box 017
Georgia College and State University
Milledgeville, GA, 31061, USA
email: laurie.battle@gcsu.edu

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