• Oscillation in odd-order neutral delay differential equations

    • Fulltext

       

        Click here to view fulltext PDF


      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/105/02/0219-0225

    • Keywords

       

      Functional differential equations; oscillation of all solutions

    • Abstract

       

      Consider the odd-order functional differential equation$$\left( {x\left( t \right) - ax\left( {t - \tau } \right)} \right)^n + p\left( t \right)f\left( {x\left( {t - \sigma } \right)} \right) = 0$$ where 0≤α<1, τ, σ∈(0, ∞),pC([0, ∞), (0, ∞)),fC1(R,R) such thatf is increasing,xf(x)>0 forx≠0 andf satisfies a generalized linear condition$$\mathop {\lim \inf }\limits_{x \to 0} \left| {\frac{{df}}{{dx}}} \right| = 1$$ Here we prove that every solution of (*) oscillates if$$\mathop {\lim \inf }\limits_{x \to 0} \int_{t - \sigma /n}^t {\sigma ^{n - 1} p\left( s \right)ds > \frac{1}{e}\left( {1 - a} \right)\left( {n - 1} \right)!\left( {\frac{n}{{n - 1}}} \right)^{n - 1} } $$ This result generalizes a recent result of Gopalsamyet al. [6].

    • Author Affiliations

       

      Pitambar Das1

      1. Department of Mathematics, Indira Gandhi Institute of Technology, Sarang, Talcher, Orissa, India
    • Dates

       
  • Proceedings – Mathematical Sciences | News

    • Editorial Note on Continuous Article Publication

      Posted on July 25, 2019

      Click here for Editorial Note on CAP Mode

© 2021-2022 Indian Academy of Sciences, Bengaluru.