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Two positive solutions of a boundary value problem for difference equations. (English) Zbl 0854.39001
The paper deals with the boundary value problem \(- \Delta^2 y(t - 1) = f(t,y (t))\), \(\alpha y(0) = \beta y (0)\), \(\gamma y (b + 1) = - \delta \Delta y(b + 1)\), where \(\alpha, \beta, \gamma \geq 0\), \(\delta > 0\), \(b \geq 2\), \(\alpha \gamma (b + 1) + \alpha \delta + \beta \gamma > 0\), \(t = 1, 2, \dots, b + 1\), and where \(f\) is continuous with respect to \(y \in \mathbb{R}^n\). Under additional assumptions, the existence of two positive solutions lying in a certain cone is proved. The analogous continuous case was considered by L. H. Erbe and H. Wang [Proc. Am. Math. Soc. 120, No. 3, 743-748 (1994; Zbl 0802.34018)].
Reviewer: L.Berg (Rostock)

MSC:
39A10 Additive difference equations
39A12 Discrete version of topics in analysis
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References:
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