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

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.