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Oscillation criteria for odd‐order nonlinear delay differential equations with a middle term
Author(s) -
Grace S. R.,
Jadlovská I.,
Zafer A.
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4377
Subject(s) - mathematics , oscillation (cell signaling) , delay differential equation , term (time) , order (exchange) , nonlinear system , differential equation , work (physics) , third order , mathematical analysis , type (biology) , calculus (dental) , law , physics , ecology , genetics , finance , quantum mechanics , economics , biology , thermodynamics , medicine , dentistry , political science
The oscillation of solutions of the n th‐order delay differential equationr 2 ( t )r 1 ( t )y ( n − 2 ) ( t )α′′ + p ( t )y ( n − 2 ) ( t )α + q ( t ) f ( y ( g ( t ) ) ) = 0was studied in [S. R. Grace and A. Zafer, Math. Meth. Appl. Sci. 2016, 39 1150–1158] when n is even and the n odd case has been referred to as an interesting open problem. In the present work, our primary aim is to address this situation. Our method of the proof that is quite different from the aforementioned study is essentially new. We introduce V n −1 ‐type solutions and use comparisons with first‐order oscillatory and second‐order nonoscillatory equations. Examples are given to illustrate the main results. Copyright © 2017 John Wiley & Sons, Ltd.