Abstract
This study aims to present some new sufficient conditions for the oscillatory behavior of solutions to a class of second order half-linear functional dynamic equations with mixed neutral term i.e., the neutral term contains both retarded and advanced arguments. The results obtained are applicable in the case where the studied equation has unbounded neutral coefficients and they are new even for the linear case. Illustrative examples are also provided.
Highlights
In this study, we are concerned with the oscillation of second order half-linear mixed neutral dynamic equations of the form r(t) y (t)Xn + qi(t)x hi(t) = 0; t 2 [t0; 1)T i=1 (1.1)where n 1 is an integer, is a ratio of positive odd integers, T is a time scale unbounded above with t0 2 T, and y t := x t + p1 t x 1(t) + p2 t x 2(t) : (1.2)For some basic facts on time scale calculus and dynamic equations on time scales, one may consult the excellent texts by Bohner and Peterson [8, 9]
This study aims to present some new su¢ cient conditions for the oscillatory behavior of solutions to a class of second order half-linear functional dynamic equations with mixed neutral term i.e., the neutral term contains both retarded and advanced arguments
The results obtained are applicable in the case where the studied equation has unbounded neutral coe¢ cients and they are new even for the linear case
Summary
This study aims to present some new su¢ cient conditions for the oscillatory behavior of solutions to a class of second order half-linear functional dynamic equations with mixed neutral term i.e., the neutral term contains both retarded and advanced arguments. The results obtained are applicable in the case where the studied equation has unbounded neutral coe¢ cients and they are new even for the linear case. We are concerned with the oscillation of second order half-linear mixed neutral dynamic equations of the form r(t) y (t)
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