Criticality of general two-term even-order linear difference equation via a chain of recessive solutions

Abstract

In this paper, the author investigates particular disconjugate even-order linear difference equations with two terms and classify them based on the properties of their recessive solutions at plus and minus infinity. The main theorem described states that the studied equation is $(k-p+1)$-critical whenever a specific second-order linear difference equation is $p$-critical. In the proof, the author derived closed-form solutions for the studied equation wherein the solutions of the said second-order equation appear. Furthermore, the solutions were organized, in order to determine recessive solutions, into a linear chain by sequence ordering that compares the solutions at $\pm \infty$.