## Nonoscillation and asymptotic behaviour for forced nonlinear third order differential equations.(English)Zbl 0581.34026

The equation (*) $$(r(t)y'')'+q(t)(y')^{\gamma}+p(t)y^{\beta}=f(t)$$ is considered, where p,q,r and f are real-valued continuous functions on [0,$$\infty)$$ such that p(t)$$\geq 0$$, q(t)$$\geq 0$$, $$r(t)>0$$ and f(t)$$\geq 0$$ and each of $$\beta >0$$ and $$\gamma >0$$ is a ratio of odd integers. Sufficient conditions are obtained so that solutions of (*) are nonoscillatory. Further, the asymptotic behaviour of these nonoscillatory solutions are studied.

### MSC:

 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems 34E05 Asymptotic expansions of solutions to ordinary differential equations

### Keywords:

asymptotic behaviour; nonoscillatory solutions