OSCILLATION OF SECOND ORDER NEUTRAL EMDEN-FOWLER DELAY DYNAMIC EQUATIONS OF MIXED TYPE

TitleOSCILLATION OF SECOND ORDER NEUTRAL EMDEN-FOWLER DELAY DYNAMIC EQUATIONS OF MIXED TYPE
Publication TypeJournal Article
Year of Publication2009
AuthorsWANG BIYING, XU ZHITING
JournalDynamic Systems and Applications
Volume18
Start Page441
Pagination15
Date Published2009
ISSN1056-2176
AMS Subject Classification39A10
Abstract

By means of generalized Riccati transformation and averaging technique, we establish some oscillation criteria for the second-order neutral Emden-Fowler delay dynamic equation of mixed type

                                     ( r(t)x(t) )+ q1(t) |y( δ(t) )|α−1 y( δ(t) ) + q2(t) |y( δ(t) )|β−1 y( δ(t) ) = 0,

on a time scale T. Our results as a special case when T = R improve some well known oscillation criteria for second order neutral Emden-Fowler delay differential equation of mixed type, and when T = N, T = hN, and T = qNo , i.e., for neutral delay difference equations, neutral delay difference equations with constant step size, and q-neutral difference equations with variable step size. The results obtained here are essentially new and can be applied to different types of time scales. Some applications and examples are considered to illustrate the main results.

PDFhttps://acadsol.eu/dsa/articles/18/31-DSA-165.pdf
Refereed DesignationRefereed