## Periodic solutions of the third order parametric differential equations involving large nonlinearities.(English)Zbl 0753.34025

Summary: Sufficient conditions are obtained for the existence of periodic solutions to the triad of parametric third order equations $$x'''+L(t,x)=a(x'')$$, $$x'''+L(t,x)=b(x')$$, $$x'''+L(t,x)=c(x)$$, where $$L(t,x):=f(x)x''+g(t)x'+h(x)+p(t)+q(t,x,x',x'')$$. The main endeavour is that the involved nonlinearities $$a(x'')$$ or $$b(x')$$ or $$c(x)$$ be not restricted too much. Uniqueness and instability criteria are established in special cases as well.

### MSC:

 34C25 Periodic solutions to ordinary differential equations 34D20 Stability of solutions to ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems
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### References:

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