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Oscillation criteria for a nonlinear difference equation

โœ Scribed by Wan Tong Li; Sui Sun Cheng


Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
357 KB
Volume
36
Category
Article
ISSN
0898-1221

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Sufficient conditions for the oscillation of all solutions of a damped difference equation of the form A2yn+pnAyn+qnf(yn+l)=O, n = 0,1,2,..., are obtained. No sign conditions on the sequences {pn} and {qn} are assumed. Examples are inserted in the text to illustrate our results.

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## This paper is concerned with the nonlinear partial difference equation with continuous variables m A(x + a, y) + A(x, y + a) -A(x, y) + E hi(x, y, A(x -ai, y -~-i)) -~ 0, i=l where a, ai, ri are positive numbers, hi(x,y,u) E C(R + ร— R + x R, R), uhi(x, y, u) > 0 for u ยข 0, hi is nondecreasing i

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Several oscillation criteria are established for the second-order damped nonlinear difference equation where a > 0 is any quotient of odd integers, {pโ€ข} and {qn} are real sequences, and f E C(R, R) such that xf(x) > 0 for x # 0. Several examples which dwell upon the importance of our results are al