We study the unilateral global bifurcation result for the one-dimensional discrete p-Laplacian problem {−Δ[φp(Δu(t−1))]=λa(t)φp(u(t))+g(t,u(t),λ),t∈[1,T+1]Z,Δu(0)=u(T+2)=0,\documentclass[12pt]{minimal}
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\begin{document}$$ \textstyle\begin{cases} -\Delta [\varphi _{p}(\Delta u(t-1))]=\lambda a(t)\varphi _{p}(u(t))+g(t,u(t), \lambda ),\quad t\in [1,T+1]_{Z}, \\ \Delta u(0)=u(T+2)=0, \end{cases} $$\end{document} where Δu(t)=u(t+1)−u(t)\documentclass[12pt]{minimal}
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\begin{document}$\Delta u(t)=u(t+1)-u(t)$\end{document} is a forward difference operator, φp(s)=|s|p−2s\documentclass[12pt]{minimal}
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\begin{document}$\varphi _{p}(s)=|s|^{p-2}s$\end{document} (1<p<+∞\documentclass[12pt]{minimal}
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\begin{document}$1< p<+\infty $\end{document}) is a one-dimensional p-Laplacian operator. λ is a positive real parameter, a:[1,T+1]Z→[0,+∞)\documentclass[12pt]{minimal}
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\begin{document}$a: [1,T+1]_{Z}\to [0,+\infty )$\end{document} and a(t0)>0\documentclass[12pt]{minimal}
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\begin{document}$a(t_{0})>0$\end{document} for some t0∈[1,T+1]Z\documentclass[12pt]{minimal}
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\begin{document}$t_{0}\in [1,T+1]_{Z}$\end{document}, g:[1,T+1]Z×R2→R\documentclass[12pt]{minimal}
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\begin{document}$g :[1,T+1]_{Z}\times \mathbb{R}^{2}\to \mathbb{R}$\end{document} satisfies the Carathéodory condition in the first two variables. We show that (λ1,0)\documentclass[12pt]{minimal}
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\begin{document}$(\lambda _{1},0)$\end{document} is a bifurcation point of the above problem, and there are two distinct unbounded continua C+\documentclass[12pt]{minimal}
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\begin{document}$\mathscr{C}^{+}$\end{document} and C−\documentclass[12pt]{minimal}
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\begin{document}$\mathscr{C}^{-}$\end{document}, consisting of the bifurcation branch C\documentclass[12pt]{minimal}
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\begin{document}$\mathscr{C}$\end{document} from (λ1,0)\documentclass[12pt]{minimal}
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\begin{document}$(\lambda _{1},0)$\end{document}, where λ1\documentclass[12pt]{minimal}
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\begin{document}$\lambda _{1}$\end{document} is the principal eigenvalue of the eigenvalue problem corresponding to the above problem. Let T>1\documentclass[12pt]{minimal}
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\begin{document}$T>1$\end{document} be an integer, Z denote the integer set for m,n∈Z\documentclass[12pt]{minimal}
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\begin{document}$m, n\in Z$\end{document} with m<n\documentclass[12pt]{minimal}
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\begin{document}$m< n$\end{document}, [m,n]Z:={m,m+1,…,n}\documentclass[12pt]{minimal}
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\begin{document}$[m, n]_{Z}:=\{m, m+1,\ldots , n\}$\end{document}.
