Our focus in this study revolves around investigating of a discrete fractional p-Schrödinger–Kirchhoff equation with a parameter \(\begin{aligned} (a+b[u]^{p}_{s, p})(-\Delta _{\mathcal {G}})^{s}_{p}u(\xi )+\lambda V(\xi )\vert u(\xi )\vert ^{p-2}u(\xi )=f(\xi , u(\xi )),\ \ \text {for}\ \xi \in \mathbb {Z} \end{aligned}\) where \(a,\ b>0\) and \(0<s<1<p<\infty \) are constants, \(\lambda \) is a parameter, \((-\Delta _{\mathcal {G}})^{s}_{p}\) is the fractional discrete p-Laplace operator, the nonlinearity \(f\in C(\mathbb {Z}\times \mathbb {R}, \mathbb {R})\) requires some assumptions which will be listed later and \(V{:}\,\mathbb {Z}\longmapsto \mathbb {R}^{+}\) is a potential function. Combining variational approaches such that mountain pass theorem and symmetric mountain pass theorem, we establish the existence and multiplicity of homoclinic solutions for our problem.
