Sturmian comparison theory for half-linear and nonlinear differential equations via Picone identity

Ozbekler A.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, cilt.40, sa.8, ss.3100-3110, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 40 Sayı: 8
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1002/mma.4224
  • Dergi Adı: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.3100-3110
  • Ankara Üniversitesi Adresli: Hayır

Özet

In this paper, Sturmian comparison theory is developed for the pair of second-order differential equations; first of which is the nonlinear differential equations of the form (m(t) Phi(beta)(y'))' + Sigma(n)(i=1) q(i)(t) Phi(alpha i)(y) = 0 and the second is the half-linear differential equations (k(t)Phi(beta)(x'))' + p(t)Phi(beta)(x) = 0 where Phi(alpha)(s) = vertical bar s vertical bar(alpha-1)s and alpha(1) > ... > alpha(m) > beta > alpha(m+1) > ... > alpha(n) > 0. Under the assumption that the solution of has two consecutive zeros, we obtain Sturm-Picone type and Leighton type comparison theorems for by employing the new nonlinear version of Picone formula that we derive. Wirtinger type inequalities and several oscillation criteria are also attained for (1). Examples are given to illustrate the relevance of the results. Copyright (c) 2016 John Wiley & Sons, Ltd.