The second-order nonlocal difference equation $-A\left(\sum _{j=1}^N{\alpha }_j((\mathrm{\Delta }u)\left(t_j\right){)}^q\right){\mathrm{\Delta }}^{2}u(n)=\lambda f(u(n)),n\in \{0,1,2,\dots ,b\}$is considered subject to the right-focal boundary conditions $u(0)=0=(\mathrm{\Delta }u)(b+1).$The problem is a discrete version of a one-dimensional Kirchhoff-type equation. Existence of at least one positive solution is considered by means of a topological fixed-point theory. Weaker-than-usual conditions are proposed for the coefficient function A.

中文翻译：

---

具有符号变化系数的离散基尔霍夫方程

二阶非局部差分方程 $-\mathrm{一种}\left(\sum _{j=1}^N{\alpha }_j((\mathrm{\Delta }你)\left({吨}_j\right){)}^q\right){\mathrm{\Delta }}^2你(n)=\lambda F(你(n)),n\in \{0,1,2,\dots ,乙\}$被认为受右焦边界条件的约束 $你(0)=0=(\mathrm{\Delta }你)(乙+1).$该问题是一维基尔霍夫型方程的离散版本。通过拓扑不动点理论考虑至少一个正解的存在。为系数函数A提出了比通常更弱的条件。