TY  - JOUR
ID  - Ricceri2025
LB  - Ricceri2025
AU  - Ricceri, Biagio
TI  - A note on nonlocal discrete problems involving sign-changing Kirchhoff functions
ST  - A note on nonlocal discrete problems involving sign-changing Kirchhoff functions
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2025
VL  - 45
IS  - 5
SP  - 657
EP  - 663
DO  - https://doi.org/10.7494/OpMath.2025.45.5.657
UR  - https://doi.org/10.7494/OpMath.2025.45.5.657
AB  - 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) \(b\gt 0\).
KW  - minimax theorems
KW  - Kirchhoff functions
KW  - difference equations
KW  - variational methods
KW  - multiplicity of solutions
SN  - 1232-9274
ER  -