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.

Abstract

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),  t≥t0, and (r(t)y′′(t))′+q(t)k(y′(t))+p(t)h(y(g(t)))=f(t),  t≥t0, 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.