## Positive periodic solutions for nonlinear difference equations with periodic coefficients.(English)Zbl 0923.39010

The authors consider the following boundary value problem $-\Delta [p(n-1)\Delta y(n-1)]+q(n) y(n)=f(n,y(n)), \quad n=1,2,\dots,N,$
$y(0)=y(N),\qquad p(0)\Delta y(0)=p(N)\Delta y(N).$ Using a fixed point theorem in cones, existence of one as well as two solutions is established for the boundary value problem. The authors also consider the boundary value problem with a parameter. Finally, existence of positive periodic solutions on the whole discrete axis is established when the coefficients of the boundary value problem are periodic.

### MSC:

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

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