Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1097.39003
Saker, S.H.
Oscillation of second-order nonlinear neutral delay dynamic equations on time scales. (English)
[J] J. Comput. Appl. Math. 187, No. 2, 123-141 (2006). ISSN 0377-0427

This paper deals with second-order nonlinear neutral delay dynamic equations of the form $$ (r(t)([y(t)+p(t)y(t-\tau)]^\Delta)^\gamma)^\Delta+f(t,y(t-\delta))=0 $$ on time scales ${\Bbb T}$ satisfying the implication $t\in{\Bbb T}\,\Rightarrow\,t-\delta,t-\tau\in{\Bbb T}$ for all $t\in{\Bbb T}$, where $\tau,\delta$ are positive reals. The reviewer wants to point out that in case $\delta>0$ or $\tau>0$ this implies bounded graininess of the time scale ${\Bbb T}$ under consideration. Moreover, $\gamma\geq 1$ is an odd integer, the positive coefficient functions $r,p$ are assumed to be $rd$-continuous where $r$ satisfies some integrability condition, $p(t)\in[0,1)$ and the nonlinearity $f$ is continuous satisfying some positive feedback property. The author provides various sufficient oscillation criteria for the above equation, in particular of Philos- and Kamenev-type. From these general results, certain special cases for particular time scales are deduced. Referring to the above remark on bounded graininess, Corollaries 4.5 and 4.6 are only applicable in the delay-free case $\delta=\tau=0$. Finally, three examples illustrate the paper.
[Christian Pötzsche (Minneapolis)]

MSC 2000:: *34K11 Oscillation theory of functional-differential equations
34K40 Neutral equations
39A10 Difference equations

Keywords: oscillation; time scale; second-order nonlinear neutral delay dynamic equations

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]