Uniqueness intervals and two-point boundary value problems

Grant B. Gustafson


 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.

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DOI: https://doi.org/10.2478/tatra.v43i0.10