“…2 Department of Mathematics, Texas A&M University-Kingsville, 700 University Blvd., Kingsville, TX 78363-8202, USA. 3 Department of Mathematics and Statistics, Missouri S&T, Rolla, MO 65409-0020, USA.…”
Section: And δ(T) = T Note That R(t) = T - Let η(T) = /T and A(tmentioning
This paper is concerned with oscillatory behavior of a certain class of second-order neutral delay dynamic equationson a time scale T with sup T = ∞, where 0 ≤ p(t) ≤ p 0 < ∞. Some new results are presented that not only complement and improve those related results in the literature, but also improve some known results for a second-order delay dynamic equation without a neutral term. Further, the main results improve some related results for second-order neutral differential equations.
“…2 Department of Mathematics, Texas A&M University-Kingsville, 700 University Blvd., Kingsville, TX 78363-8202, USA. 3 Department of Mathematics and Statistics, Missouri S&T, Rolla, MO 65409-0020, USA.…”
Section: And δ(T) = T Note That R(t) = T - Let η(T) = /T and A(tmentioning
This paper is concerned with oscillatory behavior of a certain class of second-order neutral delay dynamic equationson a time scale T with sup T = ∞, where 0 ≤ p(t) ≤ p 0 < ∞. Some new results are presented that not only complement and improve those related results in the literature, but also improve some known results for a second-order delay dynamic equation without a neutral term. Further, the main results improve some related results for second-order neutral differential equations.
We consider the asymptotic behavior of solutions to a class of third-order neutral differential equations with distributed deviating arguments. Our criteria extend the related results reported in the literature. An illustrative example is included.
“…China. 2 LinDa Institute of Shandong Provincial Key Laboratory of Network Based Intelligent Computing, Linyi University, Linyi, Shandong 276005, P.R. China.…”
Section: Assume First That Case (I) Holds It Follows From Z (T) > mentioning
The objective of this paper is to study asymptotic nature of a class of third-order neutral delay differential equations. By using a generalized Riccati substitution and the integral averaging technique, a new Philos-type criterion is obtained which ensures that every solution of the studied equation is either oscillatory or converges to zero. An illustrative example is included. MSC: 34K11
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