Consider a linear $n$th order differential equation with continuous coefficients and continuous forcing term. The maximal uniqueness interval for a classical $2$-point boundary value problem will be calculated by an algorithm that uses an auxiliary linear system of differential equations, called a Mikusinski system. This system always has higher order than $n$. The algorithm leads to a graphical representation of the uniqueness profile and to a new method for solving $2$-point boundary value problems. The ideas are applied to construct a graphic for the conjugate function associated with the $n$th order linear homogeneous differential equation. Details are given about how to solve classical $2$-point boundary value problems, using auxiliary Mikusinski systems and Green's function.
@article{10,
title = {Uniqueness intervals and two-point boundary value problems},
journal = {Tatra Mountains Mathematical Publications},
volume = {43},
year = {2009},
doi = {10.2478/tatra.v43i0.10},
language = {EN},
url = {http://dml.mathdoc.fr/item/10}
}
Gustafson, Grant B. Uniqueness intervals and two-point boundary value problems. Tatra Mountains Mathematical Publications, Tome 43 (2009) . doi : 10.2478/tatra.v43i0.10. http://gdmltest.u-ga.fr/item/10/