# Criterion of $p$-criticality for one term $2n$-order difference operators

## Petr Hasil

Address: Department of Mathematics, Mendel University in Brno, Zemědělská 1, CZ-613 00 Brno, Czech Republic

E-mail: hasil@mendelu.cz

Abstract: We investigate the criticality of the one term $2n$-order difference operators $l(y)_k = \Delta ^n (r_k \Delta ^n y_k)$. We explicitly determine the recessive and the dominant system of solutions of the equation $l(y)_k = 0$. Using their structure we prove a criticality criterion.

AMSclassification: primary 39A10; secondary 39A21, 39A70, 47B25.

Keywords: one term difference operator, recessive system of solutions, p-critical operator, sub/supercritical operator.