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Oscillation of certain partial difference equations. (English) Zbl 0931.39003

Different conditions are given under which the equation \[ aA_{m+ 1,n+1} +bA_{m+1,n}+ cA_{m,n+1}- dA_{m,n}+ P_{m,n}A_{m-k,n-l}=0 \] with positive coefficients has only oscillating solutions. The results are transferred to the equation \[ A_{m+1,n+1}+ A_{m+1,n}+ A_{m,n+1}-A_{m,n}+ P_{m,n} f(A_{m-k,n-l})=0, \] but there are also given conditions under which it has a positive solution.

MSC:

39A11 Stability of difference equations (MSC2000)
39A10 Additive difference equations
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