## Dynamical systems modelled by third order differential equations with special respect to the influence of the restoring term on the properties of solutions.(English)Zbl 0706.34032

For the equations: $x'''+f(x')x''+g(x)x'+h(x)=0\quad (Li\acute enard),$
$x'''+f(x'')+g(x')+h(x)=0\quad (Rayleigh)$ conditions are given ensuring that: a) all solutions are ultimately bounded, and b) there is some solution which is unbounded.
Reviewer: E.O.Roxin

### MSC:

 34C11 Growth and boundedness of solutions to ordinary differential equations 37-XX Dynamical systems and ergodic theory 34C25 Periodic solutions to ordinary differential equations

### Keywords:

third order differential equation; bounded solutions
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### References:

 [1] Barbashin E. A., Tabueva V. A.: Dynamical System with Cylindrical Phase Space. Nauka, Moscow, 1969 · Zbl 0212.43404 [2] Reissig R., Sansone G., Conti R.: Qualitative Theorie nichtlinearerer Differentialgleichungen. Cremonese, Roma, 1963. · Zbl 0114.04302 [3] Barbashin E. A.: Liapunov Functions. Moscow, Nauka, 1970 [4] Voráček J.: Über D’-divergente Lösungen der Differentialgleichung $$x^{(n)}= f(x,x',\ldots, x^{(n-1)}; t)$$. Acta UPO 41 (1973), 83-89.
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