| Summary: | Let T>1T\gt 1 be an integer, T≔[1,T]Z={1,2,…,T},Tˆ≔{0,1,…,T+1}{\mathbb{T}}:= {{[}1,T]}_{{\mathbb{Z}}}=\{1,2,\ldots ,T\},\hspace{.0em}\hat{{\mathbb{T}}}:= \{0,1,\ldots ,T+1\}. In this article, we are concerned with the global structure of the set of sign-changing solutions of the discrete second-order boundary value problem{Δ2u(x−1)+λh(x)f(u(x))=0,x∈T,u(0)=u(T+1)=0,\left\{\begin{array}{l}{\mathrm{\Delta}}^{2}u(x-1)+\lambda h(x)f(u(x))=0,\hspace{1em}x\in {\mathbb{T}},\\ u(0)=u(T+1)=0,\end{array}\right.where λ>0\lambda \gt 0 is a parameter, f∈C(ℝ,ℝ)f\in C({\mathbb{R}},{\mathbb{R}}) satisfies f(0)=0,sf(s)>0f(0)=0,\hspace{.1em}sf(s)\gt 0 for all s≠0s\ne 0 and h:Tˆ→[0,+∞)h:\hat{{\mathbb{T}}}\to {[}0,+\infty ). By using the directions of a bifurcation, we obtain existence and multiplicity of sign-changing solutions of the above problem for λ\lambda lying in various intervals in ℝ{\mathbb{R}}. Moreover, we point out that these solutions change their sign exactly k−1k-1 times, where k∈{1,2,…,T}k\in \{1,2,\ldots ,T\}.
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