Lyapunov type inequalities for second order forced mixed nonlinear impulsive differential equations

Agarwal R. P., Ozbekler A.

APPLIED MATHEMATICS AND COMPUTATION, cilt.282, ss.216-225, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Derleme
  • Cilt numarası: 282
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1016/j.amc.2016.02.015
  • Dergi Adı: APPLIED MATHEMATICS AND COMPUTATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.216-225
  • Ankara Üniversitesi Adresli: Hayır

Özet

In this paper, we present some new Lyapunov and Hartman type inequalities for second order forced impulsive differential equations with mixed nonlinearities: x ''(t) + p(t)vertical bar x(t)vertical bar(beta-1)x(t) + q(t)vertical bar x(t)vertical bar(gamma-1)x(t) = f(t), t not equal theta(i); Delta x'(t) + p(i)vertical bar x(t)vertical bar(beta-1)x(t) + q(i)vertical bar x(t)vertical bar(gamma-1) x(t) = f(i), t = theta(i), where p, q, f are real-valued functions, {p(i)}, {q(i)}, {f(i)} are real sequences and 0 < gamma < 1 < beta < 2. No sign restrictions are imposed on the potential functions p, q and the forcing term f and the sequences {p(i)}, {q(i)}, {f(i)}. The inequalities obtained generalize and complement the existing results for the special cases of this equation in the literature. (C) 2016 Elsevier Inc. All rights reserved.