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.
Dr. Britney Hopkins
"The Existence of Solutions to a System of Nonhomogeneous Difference Equations,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 24:
2, Article 1.
Available at: https://scholar.rose-hulman.edu/rhumj/vol24/iss2/1