Three solutions of constant sign for a system of discrete equations (Q1771175)

The authors prove the existence of at least three constant solutions of the following system of discrete equations \[ u_i(k)=\sum_{\ell= 0}^N g_i(k,\ell)P_i(\ell,u_i(\ell,\dots,u_n(\ell)),\quad k=0,1,\dots,T,\;i=1,\dots,n,\;N\in\mathbb N\cup\{\infty\}. \] In the proofs different types of Krasnoselskii's fixed point theorem (Leggett-Williams, Avery, five functional) are employed. The setting for the main result is quite general, so in the second part the authors discuss numerous special cases.