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Green’s matrices and positive solutions of a discrete boundary value problem. (English) Zbl 0839.39002
Two theorems related to the existence of positive solutions of the boundary value problem $- \Delta \bigl[ P(t - 1) \Delta y(t - 1) \bigr] = f \bigl( t,y(t) \bigr)$ are proved. In particular when $$f(t,y(t)) = 0$$ it is shown that the above problem has only the trivial solution and the corresponding Green’s function exists.

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