Some sufficient conditions are obtained for the oscillation of forced neutral differential equations with positive and negative coefficients
Oscillations of solutions of neutral differential equations with positive and negative coefficients
β Scribed by J.H. Shen; L. Debnath
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 440 KB
- Volume
- 14
- Category
- Article
- ISSN
- 0893-9659
No coin nor oath required. For personal study only.
β¦ Synopsis
obtain some new results for oscillation of all solutions of the neutral differential equation with positive and negative coefficients i [y(t) -R(Mt -r)l + P(Mt -7) -Q(Mt -0) = 0, where P,Q, R E C([to, co),R), r E (O,m), and r,(~ E [O,w). These new results are obtained by establishing and using some new lemmas which are interesting in their own right and which may have further applications in analysis.
π SIMILAR VOLUMES
t ## Ε½ . , β¦ g R , G β¦ , are obtained where R t q H Q u du y 1 is allowed to x Ο± w Ε½ . Ε½ oscillate and the condition H s P s y Q s y q β¦ H P u y Q u y q t s 0 .x β¦ du ds s Ο± is not necessary. Some examples are given, which show that the results here are almost sharp.
In this paper, we consider the following higher-order neutral functional differential equations with positive and negative coefficients: -& [z(t) + cx (t -T)l + (-1) \*+l [P(t)?2 (t -CT) -Q(t)2 (t -a)] = 0, t 2 to, where n > 1 is an integer, c E R, ~,o,6 E W+, and P,Q E C([to,m),W+), IR+ = [O ,oo).
In this paper, we investigate the oscillation and nonoscillation of the neutral difference equation with variable coefficients where pn,qn, c~n (n = 0,1,2,...) are real numbers with pn >\_ 0, qn >\_ 0, cn \_> 0, k, l, and r are integers with 0 < I < k -1, r > 0, Pn -qn-k+l ~--0, and not identically