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Oscillation of first‐order dynamic equations with nonmonotone delay
Author(s) -
Öcalan Özkan
Publication year - 2019
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.6165
Subject(s) - mathematics , dynamic equation , oscillation (cell signaling) , order (exchange) , monotone polygon , first order , mathematical analysis , mathematical physics , physics , nonlinear system , geometry , quantum mechanics , genetics , finance , economics , biology
Consider the first‐order dynamic equationsx Δ ( t ) + p ( t ) x τ ( t ) = 0 , t ∈ [ t 0 , ∞ ) Twhere p ∈ C r d[ t 0 , ∞ ) T , R +,τ ∈ C r d[ t 0 , ∞ ) T , Tand τ ( t ) ≤ t ,lim t → ∞ τ ( t ) = ∞ . Under the assumption that the τ ( t ) is not necessarily monotone, we present new sufficient conditions for the oscillation of first‐order delay dynamic equations on time scales.