Publikationsdatum:
1992-01-01
Beschreibung:
Consider the difference equationsΔmxn+(−1)m+1pnf(xn−k)=0, n=0,1,… (1)andΔmyn+(−1)m+1qng(yn−ℓ)=0, n=0,1,…. (2)We establish a comparison result according to which, whenmis odd, every solution of Eq.(1) oscillates provided that every solution of Eq.(2) oscillates and, whenmis even, every bounded solution of Eq.(1) oscillates provided that every bounded solution of Eq.(2) oscillates. We also establish a linearized oscillation theorem according to which, whenmis odd, every solution of Eq.(1) oscillates if and only if every solution of an associated linear equationΔmzn+(−1)m+1pzn−k=0, n=0,1,… (*)oscillates and, when m is even, every bounded solution of Eq.(1) oscillates if and only if every bounded solution of (*) oscillates.
Print ISSN:
0161-1712
Digitale ISSN:
1687-0425
Thema:
Mathematik
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