Green’s matrices and positive solutions of a discrete boundary value problem. (English) Zbl 0839.39002

Merdivenci, Ferhan

Panam. Math. J. 5, No. 1, 25-42 (1995).

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.

Reviewer: B.M.Agrawal (Gwalior)

MSC:

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

Keywords:

Green’s matrices; positive solutions; boundary value problem; Green’s function