Open AccessUnbounded oscillation of higher-order nonlinear delay dynamic equations of neutral type with oscillating coefficients
Author(s) -
Başak Karpuz
Publication year - 2009
Publication title -
electronic journal of qualitative theory of differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.524
H-Index - 33
ISSN - 1417-3875
DOI - 10.14232/ejqtde.2009.1.34
Subject(s) - mathematics , oscillation (cell signaling) , type (biology) , nonlinear system , order (exchange) , dynamic equation , mathematical analysis , control theory (sociology) , physics , control (management) , computer science , ecology , genetics , biology , finance , quantum mechanics , artificial intelligence , economics
In this paper, we present a criterion on the oscillation of unbounded solutions for higher-order dynamic equations of the following form: x(t) + A(t)x( (t)) n large t. We give change of order formula for double(iterated) integrals to prove our main result. Some simple examples are given to illustrate the applicability of our results too. In the literature, almost all of the results for (?) with T = R and T = Z hold for bounded solutions. Our results are new and not stated in the literature even for the particular cases T = R and/or T = Z.
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