Zou, Huichao; Jiang, Hefeng; Zhang, Xinguang Nonlinear eigenvalue problems for BVPs of second-order difference equations. (English) Zbl 1120.39012 Nonlinear Funct. Anal. Appl. 11, No. 4, 523-531 (2006). Using the Krasnoselskii fix point theorem, the authors give sufficient conditions for the existence of at least one positive solution of the boundary value problem \(x(0) = x(T+2)= 0\) for the second-order difference equation \[ \Delta^2 x(t-1) + \lambda f(t,x(t)) = 0, \;t \in \{1,2,...,T+1\}, \] where \(\Delta x(t) = x(t+1) - x(t),\) \(T \geq 2\) is a given integer. Reviewer: Victor I. Tkachenko (Kyïv) MSC: 39A11 Stability of difference equations (MSC2000) 39A12 Discrete version of topics in analysis 34L30 Nonlinear ordinary differential operators Keywords:second order difference equation; boundary value problem; positive solution PDFBibTeX XMLCite \textit{H. Zou} et al., Nonlinear Funct. Anal. Appl. 11, No. 4, 523--531 (2006; Zbl 1120.39012)