Oscillation criteria for first-order neutral nonlinear difference equations with variable coefficients
โ Scribed by Wan-Tong Li
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 361 KB
- Volume
- 10
- Category
- Article
- ISSN
- 0893-9659
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โฆ Synopsis
consider the first-order neutral nonlinear difference equation of the form A (in -pnyn-r) + qn ijI IY,-0, Ia' sgn Y~-~, = 0, R = 0, 1,
where T > 0, t~i 2 0 (i = 1,2,. . ,m) are integers, {p,} and {qn} are nonnegative sequences. We obtain new criteria for the oscillation of the above equation without the restrictions Crzo q,, = 03
or crzo nqn CT="=, qj = co commonly used in the literature.
๐ SIMILAR VOLUMES
The purpose of this paper is to study nonoscillations and oscillations of first order neutral equations with variable coefficients. We obtain several new existence theorems of nonoscillatory solutions and a sufficient condition for all solutions of such equations to oscillate. Our conditions are "sh
t ## ลฝ . , โฆ g R , G โฆ , are obtained where R t q H Q u du y 1 is allowed to x ฯฑ w ลฝ . ลฝ oscillate and the condition H s P s y Q s y q โฆ H P u y Q u y q t s 0 .x โฆ du ds s ฯฑ is not necessary. Some examples are given, which show that the results here are almost sharp.
## This paper discusses a class of first-order neutral differential equations with variable coefficients and variable deviations. A series of sufficient conditions are established for all solutions of the equations to be oscillatory, and some of the conditions are sharp.
In this paper, some sufficient conditions are obtained for the oscillation of all solutions of even-order nonlinear neutral differential equations with variable coefficients. Our results improve and generalize known results. In particular, the results are new even when n = 2.