<abstract xmlns="http://www.w3.org/1999/xhtml"><p> Consider a linear <italic>n</italic>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 <italic>n</italic>. 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 <italic>n</italic>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.</p></abstract>

Consider a linear nth 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 nth 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.

Uniqueness intervals and two–point boundary value problems

Department of Mathematics University of Utah 155 South 1400 East, 233JWB Salt Lake City, Utah 84112 U.S.A.

Tatra Mountains Mathematical Publications

{"article-title":"Uniqueness intervals and two\u2013point boundary value problems"}

Consider a linear nth order differential equation with continuous coefficients and continuous forcing term. The maximal uniqueness interval for a classical...

Uniqueness intervals and two–point boundary value problems

Published Online: Nov 12, 2012

Page range: 91 - 97

DOI: https://doi.org/10.2478/v10127-009-0028-3

Keywords
uniqueness, boundary value problem, Mikusinski system.

This content is open access.

Uniqueness intervals and two–point boundary value problems

Published Online: Nov 12, 2012

Page range: 91 - 97

DOI: https://doi.org/10.2478/v10127-009-0028-3

Keywordsuniqueness, boundary value problem, Mikusinski system.

This content is open access.

Keywords
uniqueness, boundary value problem, Mikusinski system.