Conjugacy of Self-Adjoint Difference Equations of Even Order

Abstract

We study oscillation properties of $2n$-order Sturm-Liouville difference equations. For these equations, we show a conjugacy criterion using the $p$-criticality (the existence of linear dependent recessive solutions at $\mathrm{\infty }$ and $-\mathrm{\infty }$). We also show the equivalent condition of $p$-criticality for one term $2n$-order equations.