Some new results on oscillation and nonoscillation for delay differential equations with impulses are established. A counterexample is given which shows that a known oscillation criterion is incorrect.
New Oscillation Criteria for Delay Difference Equations
โ Scribed by Zhiguo Luo; Jianhua Shen
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 88 KB
- Volume
- 264
- Category
- Article
- ISSN
- 0022-247X
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โฆ Synopsis
This paper considers the delay difference equation
where p n is a sequence of nonnegative real numbers and k is a positive integer. Some new oscillation criteria for this equation are obtained. Our theorems improve all known results in the literature.
๐ SIMILAR VOLUMES
In this paper, two interesting oscillation criteria are obtained for all solutions of ลฝ . the nonlinear delay difference equations of the form y y y q p f y s 0, n s 0, 1, 2, . . . . Some applications are given to demonstrate the advantage of results obtained in this paper. Our results also improve
First, we establish the equivalence of the oscillation of the delay difference equation โฌ x q p x s 0, Next, we obtain some sharp conditions for oscillations and nonoscillations of the first equation.
In this paper, new oscillation criteria are obtained for all solutions of the odd w ลฝ . ลฝ . ลฝ .x ลฝn. ลฝ . ลฝ . order neutral differential equation x t y P t x t y q Q t x t y s 0, ลฝw . . ลฝw . q . ลฝ . w . where P g C t ,ฯฑ , R , Q g C t ,ฯฑ , R , g 0, ฯฑ , g 0, ฯฑ , and n is odd. 0 0 ฯฑ n y 1 ลฝ . Our result