In this paper, discrete inequalities are used to offer sufficient conditions for oscillation of all solutions of second-order nonlinear difference equations with alternating coefficients. @ 2000 Elsevier Science Ltd. All rights reserved.
Remarks on two recent oscillation theorems for second-order linear difference equations
โ Scribed by Wan-Tong Li; Sui-Sun Cheng
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 117 KB
- Volume
- 16
- Category
- Article
- ISSN
- 0893-9659
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๐ SIMILAR VOLUMES
The authors consider second-order difference equations of the type A ((~~~)") + w&,, = 0, (E) where cz 10 is the ratio of odd positive integers, {qn} is a positive sequence, and {u(n)} is a positive increasing sequence of integers with o(n) -+ co as n + cc. They give some oscillation and comparison
In this paper discrete inequalities are used to offer sufficient conditions for the oscillation of all solutions of the difference equation ลฝ . n n n q 1 n q 1 n where 0 -s prq with p, q odd integers, or p even and q odd integers. Several examples which dwell upon the importance of our results are
A (an(Ayn)% + ยข (n, yn,Ayn) where an > O, qn > O, f, and ยข are continuous real valued functions, and uf(u) > 0 for u ยข 0. They give oscillation results for equation (E). Examples are included to illustrate the results. @ 2001 Elsevier Science Ltd. All rights reserved.