Opuscula Math. 45, no. 5 (2025), 657-663
https://doi.org/10.7494/OpMath.2025.45.5.657
Opuscula Mathematica
A note on nonlocal discrete problems involving sign-changing Kirchhoff functions
Abstract. In this note, we establish a multiplicity theorem for a nonlocal discrete problem of the type \[\begin{cases} -\left(a\sum_{m=1}^{n+1}|x_m-x_{m-1}|^2+b\right)(x_{k+1}-2x_k+x_{k-1})=h_k(x_k), &k=1,\ldots ,n, \\ x_0=x_{n+1}=0 \end{cases}\] assuming \(a\gt 0\) and (for the first time) \(b\gt 0\).
Keywords: minimax theorems, Kirchhoff functions, difference equations, variational methods, multiplicity of solutions.
Mathematics Subject Classification: 39A27, 15A63.
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- Biagio Ricceri
https://orcid.org/0009-0000-3309-411X- University of Catania, Department of Mathematics and Computer Science, Viale A. Doria 6, 95125 Catania, Italy
- Communicated by Marek Galewski.
- Received: 2025-05-13.
- Accepted: 2025-08-24.
- Published online: 2025-09-13.
