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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) v.28 n.2 Antofagasta ago. 2009

http://dx.doi.org/10.4067/S0716-09172009000200002 

Proyecciones Journal of Mathematics
Vol. 28, N° 2, pp. 125-132, August 2009.
Universidad Católica del Norte
Antofagasta - Chile



ON EXISTENCE OF PERIODIC SOLUTION TO CERTAIN NONLINEAR THIRD ORDER DIFFERENTIAL EQUATIONS


Cemil Tunq

Yüzüncü Yil University, Turkey


Correspondencia a:


Abstract

In this paper, it is investigated the existence of periodic solutions to the nonlinear third order differential equation :

x'" + c2(t)x" + c1(f)x' + f(t, x) = p(t, x, x', x").

The Leray-Schauder principle is used to show the existence of periodic solutions of this equation.

Subjclass : [AMS] 34C25, 65L06.

Keywords : Periodic solution, nonlinear third order differential equation.



References

[1] B. Mehri & D. Shadnian, On The Existence of Periodic Solutions of a Certain Class of Second Order Nonlinear Differential Equation, Math. Inequal. Appl. 1(3), pp. 431-436, (1998).        [ Links ]

[2] D. Shadnian & B. Mehri, On The Periodic Solutions of Certain Nonlinear Third Order Differential Equations, Z. Angew. Math. Mech. (75)(2), pp. 164-166, (1995).        [ Links ]

[3] C. Tung & I. Cmar, On the existence of periodic solutions to nonlinear differential equations of second order, Differ. Uravn. Protsessy Upr. (Differential Equations and Control Processes), (3), pp. 1-6, (2008).        [ Links ]

[4] C. Tung, On the existence of periodic solutins to a certain fourth-order nonlinear differential equation. Ann. Differential Equations 25, 1, pp. 8-12 (2009).        [ Links ]

CEMIL TUNQ
Department of Mathematics
Faculty of Arts and Sciences
Yüzüncü Yil University
65080, Van
Turkey
e-mail : cemtunc@yahoo.com


Received : October 2008. Accepted : March 2009