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Abstract

This article will demonstrate a process using Fixed Point Theory to determine the existence of multiple positive solutions for a type of system of nonhomogeneous even ordered boundary value problems on a discrete domain. We first reconstruct the problem by transforming the system so that it satisfies homogeneous boundary conditions. We then create a cone and an operator sufficient to apply the Guo-KrasnoselâA˘Zskii Fixed Point Theorem. The majority of the work involves developing the constraints ´ needed to utilized this fixed point theorem. The theorem is then applied three times, guaranteeing the existence of at least three distinct solutions. Thus, solutions to this class of boundary value problems exist and are not unique.

Author Bio

In the 2019 Spring semester, Stephanie Walker began the research detailed in “The Existence of Solutions to a System of Nonhomogeneous Difference Equations” as an undergraduate student at the University of Central Oklahoma. Stephanie continued the research until she graduated in the spring of 2020 with a Bachelor of Science in Mathematics. Stephanie went on to the University of Kansas and received her Master of Arts in Mathematics degree in the spring of 2022. She is now a Lecturer/Academic Program Associate in the Kansas Algebra Program at the University of Kansas.

Alkin Huggins contributed to the research detailed in “The Existence of Solutions to a System of Nonhomogeneous Difference Equations” as an undergraduate student at the University of Central Oklahoma. Alkin graduated in the fall of 2019 with a Bachelor of Science in Actuarial Science and went on to the University of Central Florida, where he received his Master of Science in Mathematics degree in the summer of 2022. He is now an Actuarial Analyst for American Fidelity.

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