PHILOS' INEQUALITY ON TIME SCALES AND ITS APPLICATION IN THE OSCILLATION THEORY

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KARPUZ B.

MATHEMATICAL INEQUALITIES & APPLICATIONS, cilt.21, sa.4, ss.1029-1046, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 21 Sayı: 4
  • Basım Tarihi: 2018
  • Doi Numarası: 10.7153/mia-2018-21-70
  • Dergi Adı: MATHEMATICAL INEQUALITIES & APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1029-1046
  • Anahtar Kelimeler: Asymptotic behaviour, dynamic equations, higher-order, oscillation, time scales, NEUTRAL DIFFERENTIAL-EQUATIONS, DELAY DYNAMIC EQUATIONS, SUFFICIENT CONDITIONS, BEHAVIOR
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

In [Bull. Acad. Polon. Sci. Ser. Sci. Math. 29 (1981), no. 7-8, 367-370], Philos proved the following result: Let f : [t(0), infinity)(R )-> R it be an n-times differentiable function such that f((n))(t)<= 0 (not equivalent to 0) and f(t) > 0 for all t <= t(0). If f is unbounded, then f(t) >= lambda t(n-1)/(n-1)! f((n-1))(t) for all sufficiently large t, where lambda is an element of (0, 1)(R). In this work, we first present time scales unification of this result. Then, by using it, we provide sufficient conditions for oscillation and asymptotic behaviour of solutions to higher-order neutral dynamic equations.