Geodesic
Solution dependence on problem parameters for initial-value problems associated with the Stieltjes Sturm-Liouville equations
Electronic journal of differential equations, Tome 2005 (2005)
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.
Classification : 34A12, 34A30
Keywords: initial value problems, continuous dependence, linear systems 
@article{EJDE_2005__2005__a116,
     author = {Battle,  Laurie},
     title = {Solution dependence on problem parameters for initial-value problems associated with the {Stieltjes} {Sturm-Liouville} equations},
     journal = {Electronic journal of differential equations},
     year = {2005},
     volume = {2005},
     zbl = {1075.34002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a116/}
}
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Battle,  Laurie. Solution dependence on problem parameters for initial-value problems associated with the Stieltjes Sturm-Liouville equations. Electronic journal of differential equations, Tome 2005 (2005). http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a116/