• Oscillation of higher order delay differential equations

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      https://www.ias.ac.in/article/fulltext/pmsc/105/04/0417-0423

    • Keywords

       

      Odd order; delay equation; oscillation of all solutions

    • Abstract

       

      A sufficient condition was obtained for oscillation of all solutions of theodd-order delay differential equation$$x^{(n)} (t) + \sum\limits_{i = 1}^m {p_i (t)} x(t - \sigma _{_i } ) = 0,$$ wherepi(t) are non-negative real valued continuous function in [T ∞] for someT≥0 and σi,∈(0, ∞)(i = 1,2,…,m). In particular, forpi(t) =pi∈(0, ∞) andn > 1 the result reduces to$$\frac{1}{m}\left( {\sum\limits_{i = 1}^m {(p_i \sigma _i^m )^{1/2} } } \right)^2 > (n - 2)!\frac{{(n)^n }}{e},$$ implies that every solution of (*) oscillates. This result supplements forn > 1 to a similar result proved by Ladaset al [J. Diff. Equn.,42 (1982) 134–152] which was proved for the casen = 1.

    • Author Affiliations

       

      P Das1 N Misra1 2 B B Mishra1

      1. Department of Mathematics, Indira Gandhi Institute of Technology, Sarang, Talcher, Orissa, India
      2. Department of Mathematics, Berhampur University, Berhampur - 760007, India
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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