Existence theorems for a system of difference equations with \((n,p)\)-type conditions (Q1855066)

The authors consider the boundary value problem \[ \Delta^nu_i(k) +q_i\bigl(k,u_1(k), \dots,u_m(k) \bigr)=0, \] \[ \Delta^j u_j(0)= \Delta^{p_i} u_i (N+n-p_i) =0,\;0\leq k\leq N,\;0\leq j\leq n-2,\;1\leq i\leq m, \] where \(n\geq 2\), \(N \geq n-1\), \(1\leq p_i\leq n-1\). Different conditions are given such that there exist a single and a double-solution, respectively, of fixed signs.