## Periodic solutions of the third-order differential equation with right- hand side in the form of nonlinear restoring term plus general gradient- like part.(English)Zbl 0777.34029

The nonlinear differential equation $$(*)$$ $$x'''=h(x)+[f(t,x,x']'$$ is considered. In $$(*)$$, $$h\in{\mathcal C}(\mathbb{R}^ 1)$$, $$f\in{\mathcal C}^ 1(\mathbb{R}^ 3)$$ and $$f$$ is $$T$$-periodic in $$t$$. Results about $$T$$-periodic solutions of $$(*)$$ are obtained: namely sufficient conditions for the existence of a harmonic solution are worked out.

### MSC:

 34C25 Periodic solutions to ordinary differential equations
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### References:

 [1] Andres J., Voráček J.: Periodic solutions of a certain parametric third order differential equation. Kniž. odb. v\?d. sp. VUT v Brn\?, B-94 (1983), 7-11. [2] Ezeilo J.O.C.: Periodic solutions of certain third order differential equations. Atti Accad. Naz. Lincei (8) 57, 1-2 (1974), 54-60. · Zbl 0288.34036 [3] Ezeilo J.O.C.: Further results on the existence of periodic solutions of a certain third order differential equation. Atti Accad. Naz. Lincei (8) 64, 1 (1978), 48-58. · Zbl 0405.34042 [4] Hille E.: On the Landau-Kallman-Rota inequality. J. Approx. Theory 6 (1972), 117-122. · Zbl 0238.47007 [5] Reissig R.: Periodic solutions of a third order nonlinear differential equation. Ann. Mat. Pura ed Appl. 4, 92 (1972), 193-198. · Zbl 0257.34043 [6] Reissig R.: An extension of Ezeilo’s result. Ann. Mat. Pura ed Appl. 4, 92 (1972), 193-198. · Zbl 0268.34045 [7] Reissig R., Sansone G., Conti R.: Nichtlineare Differentialgleichungen höherer Ordnung. Cremonese, Roma 1969. · Zbl 0172.10801
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