Zhang, Yali Existence of positive solutions for a class of second-order difference equation Dirichlet boundary problems with sign-changing weight function. (Chinese. English summary) Zbl 1474.39044 J. Sichuan Univ., Nat. Sci. Ed. 57, No. 3, 455-458 (2020). Summary: In this paper, we study the existence of positive solutions for the nonlinear second-order difference equation Dirichlet boundary problems \({\Delta^2}u(t-1) + \lambda a(t)f(u(t)) = 0\), \(t\in [1,T]_{\mathrm{Z}}\), \(u(0)= u(T+1)=0\), where \(\Delta u(t-1) = u(t)- u(t-1)\), \(T > 2\) is an integer, \(\lambda\) is a positive parameter, \(f:[0,\infty) \to \textbf{R}\) is continuous, \(f(0) > 0\) and \(a:[1,T]_{\mathrm{Z}} \to \textbf{R}\) may change sign. The proof of the main results is based on the Leray-Schauder fixed point theorem. MSC: 39A27 Boundary value problems for difference equations 39A12 Discrete version of topics in analysis 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations Keywords:difference equation; sign-changing weight function; Leray-Schauder fixed point theorem; positive solution PDFBibTeX XMLCite \textit{Y. Zhang}, J. Sichuan Univ., Nat. Sci. Ed. 57, No. 3, 455--458 (2020; Zbl 1474.39044) Full Text: DOI