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

Parhi, N.; Parhi, S.

Bull. Inst. Math., Acad. Sin. 13, 367-384 (1985).

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