In this paper discrete inequalities are used to offer sufficient conditions for the oscillation of all solutions of the difference equation Ž . 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
Note on “Oscillation Theorems for Certain Second Order Nonlinear Difference Equations”
✍ Scribed by E. Thandapani
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 103 KB
- Volume
- 224
- Category
- Article
- ISSN
- 0022-247X
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📜 SIMILAR VOLUMES
In this paper we consider the second order nonlinear difference equation Ä 4 nondecreasing, and uf u ) 0 as u / 0, q is a real sequence. Some new n Ž . sufficient conditions for the oscillation of all solutions of 1 are obtained.
In this paper we are concerned with some new criteria for the oscillation and nonoscillation of the second-order nonhomogeneous linear difference equations of Ž . Ä 4Ä 4 Ä 4 the form ⌬ c ⌬ x q q x s f , n s 1, 2, . . . , where c , f , and q are ny 1 ny1 n n n n n n real sequences, c ) 0 for n G 0, a
1 Ž Ž .. Ž . where ) 0 is any quotient of odd integers, a g C R, 0, ϱ , q g C R, R , Ž . Ž . Ž . fgC R, R , xf x ) 0, f Ј x G 0 for x / 0. Some new sufficient conditions for Ž . the oscillation of all solutions of ) are obtained. Several examples that dwell upon the importance of our results are als