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arXiv · 2505.12790

A note on nonlocal discrete problems involving sign-changing Kirchhoff functions

Biagio Ricceri
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Abstract

In this note, we establish a multiplicity theorem for a nonlocal discrete problem of the type $$\cases{-\left(a\sum_{m=1}^{n+1}|x_m-x_{m-1}|^2+b\right)(x_{k+1}-2x_k+x_{k-1})=h_k(x_k)\hskip 10pt k=1,...,n, \cr & \cr x_0=x_{n+1}=0\cr}$$ assuming $a>0$ and (for the first time) $b<0$.

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Biagio Ricceri. 2025-05-19. A note on nonlocal discrete problems involving sign-changing Kirchhoff functions. https://arxiv.org/abs/2505.12790

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