Sturmian theory for second order differential equations with mixed nonlinearities

Ozbekler A.

APPLIED MATHEMATICS AND COMPUTATION, cilt.259, ss.379-389, 2015 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 259
  • Basım Tarihi: 2015
  • Doi Numarası: 10.1016/j.amc.2015.03.001
  • Dergi Adı: APPLIED MATHEMATICS AND COMPUTATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.379-389
  • Ankara Üniversitesi Adresli: Hayır

Özet

In the paper, Sturmian comparison theory is developed for the pair of second order differential equations; first of which is the nonlinear differential equations (m(t)y')' + s(t)y' + Sigma(n)(i=1)q(i)(t)vertical bar y vertical bar(proportional to j-1)y = 0, with mixed nonlinearities alpha(1) > ... > alpha(m) > 1 > alpha(m+1) > ... > alpha(n), and the second is the non-selfadjoint differential equations (k(t)x')' + r(t)x' + p(t)x = 0. Under the assumption that the solution of Eq. (2) has two consecutive zeros, we obtain Sturm-Picone type and Leighton type comparison theorems for Eq. (1) by employing the new nonlinear version of Picone's formula that we derive. Wirtinger type inequalities and several oscillation criteria are also attained for Eq. (1). Examples are given to illustrate the relevance of the results. (C) 2015 Elsevier Inc. All rights reserved.