## 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

Zbl 0802.34018
Full Text:

### References:

 [1] Eloe P. W., Proc. Amer. Math. Soc. 78 pp 533– (1980) [2] DOI: 10.1016/0362-546X(91)90116-I · Zbl 0731.34015 [3] DOI: 10.1006/jmaa.1994.1227 · Zbl 0805.34021 [4] DOI: 10.1090/S0002-9939-1994-1204373-9 [5] Guo D., Nonlinear problems in abstract cones (1988) · Zbl 0661.47045 [6] Hankerson D., Proc. Amer. Math. Soc. 104 pp 1204– (1988) [7] Kelley W. G., Difference Equations. An Introduction With Applications (1991) [8] Krasnosel’skii M. A., Positive solutions of operator equations (1962)
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