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.
New oscillation criteria for second order linear difference equations with positive and negative coefficients
โ Scribed by Hassan A. El-Morshedy
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 520 KB
- Volume
- 58
- Category
- Article
- ISSN
- 0898-1221
No coin nor oath required. For personal study only.
โฆ Synopsis
The oscillation of second order neutral difference equations with positive and negative coefficients of the form
is investigated. We obtain many new results using the comparison between both first order and second order difference equations. An example is given to show the strength of the obtained results.
๐ SIMILAR VOLUMES
Some sufficient conditions are obtained for oscillation of all solutions of the first-order impulsive differential equation with positive and negative coefficients Our results improve the known results in the literature.
In this study, a new companion transformation is used for the neutral delay difference equation where n โ Z, R, P, Q are nonnegative sequences and r, k, l are positive integers. New criteria, which do not need the conditions and/or for all sufficiently large n, are introduced. All the recent resu
Some new criteria for the oscillation of certain difference equations with mixed nonlinearities are established. The main tool in the proofs is an inequality due to Hardy, Littlewood, and Pรณlya.