Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 896934, 11 pages
Research Article

New Results on the Nonoscillation of Solutions of Some Nonlinear Differential Equations of Third Order

Department of Mathematics, Faculty of Arts and Sciences, Gaziosmanpaşa University, 60240 Tokat, Turkey

Received 27 July 2009; Accepted 6 November 2009

Academic Editor: Patricia J. Y. Wong

Copyright © 2009 Ercan Tunç. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We give sufficient conditions so that all solutions of differential equations (r(t)y′′(t))+q(t)k(y(t))+p(t)yα(g(t))=f(t),  tt0, and (r(t)y′′(t))+q(t)k(y(t))+p(t)h(y(g(t)))=f(t),  tt0, are nonoscillatory. Depending on these criteria, some results which exist in the relevant literature are generalized. Furthermore, the conditions given for the functions k and h lead to studying more general differential equations.