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


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


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