Mixed nonlinear oscillation of second order forced dynamic equations

GÜVENİLİR A. F., ŞAHİNER Y., Zafer A.

Dynamic Systems and Applications, cilt.19, sa.3-4, ss.635-650, 2010 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 19 Sayı: 3-4
  • Basım Tarihi: 2010
  • Dergi Adı: Dynamic Systems and Applications
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.635-650
  • Ankara Üniversitesi Adresli: Evet

Özet

By using a technique similar to the one introduced by Kong [J. Math. Anal. Appl. 229 (1999) 258-270] and employing an arithmetic-geometric mean inequality, we establish oscillation criteria for second-order forced dynamic equations on time scales containing mixed nonlinearities of the form (p(t)x Δ)Δ + q(t)xσ + Σi=1n qi(t)|xσ| α1-Ixσ = e(t), t≥ t0 where p, q, q., e : T-→ ℝ are right-dense continuous with p > 0, σ is the forward jump operator, xσ(t) := x(σ(t)), and the exponents satisfy α1 > ⋯ > αm > 1 > αm+1 > ⋯ αn > 0. The results extend many well-known interval oscillation criteria from continuous case to arbitrary time scales. © Dynamic Publishers, Inc.