Ismael Nyanquini, Brahim Moussa, and Stanislas Ouaro
Multiple Solutions For a Discrete Inclusion Involving the p(k)-Laplace Kirchhoff Type Problem
Dynamic Systems and Applications 35 (2026)   1-25

https://doi.org/10.46719/dsa2026.35.01

ABSTRACT.
In this paper, we prove the existence and multiplicity of solutions for a discrete
inclusion involving the p(k)-Laplace Kirchhoff type operator in a T-dimensional Banach space. We
establish the existence of at least one solution and of at least three solutions by using the variational
principle for locally Lipschitz functions and the linking theorem under two cases of the nonsmooth
potential, nonperiodic and periodic, respectively.

AMS (MOS) Subject Classification. 46E39, 34B15, 39A10, 39A70, 35B20,

KeyWords and Phrases. Discrete Inclusion, Multiple solutions, Kirchhoff Type Problem, Locally
Lipschitz, Discrete Boundary Value Problem, Critical Point Theory.