A note on nonlocal discrete problems involving sign-changing Kirchhoff functions
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908370155339776 |
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| author | Ricceri, Biagio |
| author_facet | Ricceri, Biagio |
| contents | 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) $b<0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_12790 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on nonlocal discrete problems involving sign-changing Kirchhoff functions Ricceri, Biagio Classical Analysis and ODEs 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) $b<0$. |
| title | A note on nonlocal discrete problems involving sign-changing Kirchhoff functions |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2505.12790 |