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Cubo (Temuco)

versión On-line ISSN 0719-0646

Cubo vol.12 no.3 Temuco  2010

http://dx.doi.org/10.4067/S0719-06462010000300010 

CUBO A Mathematical Journal Vol.12, N° 03, (153–165). October 2010

 

Existence of Periodic Solutions for a Class of Second-Order Neutral Differential Equations with Multiple Deviating Arguments1

 

CHENGJUN GUO, DONAL O’REGAN AND RAVI P. AGARWAL

School of Applied Mathematics, Guangdong, University of Technology 510006, P.R.China email: guochj817@163.com

Department of mathematics, National University of Ireland, Galway, Ireland email: donal.oregan@nuigalway.ie

Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, Florida 32901, USA email: agarwal@fit.ed


ABSTRACT

Using Kranoselskii fixed point theorem and Mawhin’s continuation theorem we establish the existence of periodic solutions for a second order neutral differential equation with multiple deviating arguments.

Key words and phrases: Periodic solution, Multiple deviating arguments, Neutral differential equation, Kranoselskii fixed point theorem, Mawhin’s continuation theorem.


RESUMEN

Usando el teorema del punto fijo de Kranoselskii y el teorema de continuación de Mawhin establecemos la existencia de soluciones periódicas de una ecuación diferencial neutral de segundo orden con argumento de desviación multiple.

Math. Subj. Class.: 34K15; 34C25.


Notas

1This project is supported by grant 10871213 from NNSF of China, by grant 06021578 from NSF of Guangdong

References

[1] CHEN, Y.S., The existence of periodic solutions for a class of neutral differential difference equations, Bull. Austral. Math. Soc., 33 (1992), 508–516.

[2] CHEN, Y.S., The existence of periodic solutions of the equation x′(t) = −f (x(t), x(t−r)), J. Math. Anal. Appl., 163 (1992), 227–237.

[3] GAINES, R.E. AND MAWHIN, J.L., Coincidence degree and nonlinear differential equation, Lecture Notes in Math., Vol.568, Springer-Verlag, 1977.        [ Links ]

[4] GUO, Z.M. AND YU, J.S., Multiplicity results for periodic solutions to delay differential difference equations via critical point theory, J. Diff. Eqns., 218 (2005), 15–35.

[5] GUO, C.J. AND GUO, Z.M., Existence of multiple periodic solutions for a class of threeorder neutral differential equations, Acta. Math. Sinica, 52(4) (2009), 737–751.

[6] GUO, C.J. AND GUO, Z.M., Existence of multiple periodic solutions for a class of secondorder delay differential equations, Nonlinear Anal-B: Real World Applications, 10(5) (2009), 3825–3972.

[7] HALE, J.K., Theory of functional differential equations, Springer-Verlag, 1977.        [ Links ]

[8] KAPLAN, J.L. AND YORKE, J.A., Ordinary differential equations which yield periodic solution of delay equations, J. Math. Anal. Appl., 48 (1974), 317–324.

[9] LI, J.B. AND HE, X.Z., Proof and generalization of Kaplan-Yorke’s conjecture on periodic solution of differential delay equations, Sci. China(Ser.A), 42 (9) (1999), 957–964

[10] LI, Y.X., Positive periodic solutions of nonlinear second order ordinary differential equations, Acta Math. Sini., 45 (2002), 482–488.

[11] LU, S.P., Existence of periodic solutions for a p-Laplacian neutral functional differential equation, Nonlinear. Anal., 70 (2009), 231–243.

[12] LI, J.W. AND WANG, G.Q., Sharp inequalities for periodic functions, Applied Math. ENote, 5 (2005), 75–83.

[13] SHU, X.B., XU, Y.T. AND HUANG, L.H., Infinite periodic solutions to a class of secondorder Sturm-Liouville neutral differential equations, Nonlinear Anal., 68 (4) (2008), 905–911.

[14] WANG, G.Q. AND YAN, J.R., Existence of periodic solutions for second order nonlinear neutral delay equations, Acta Math. Sini., 47 (2004), 379–384.

[15] XU, Y.T. AND GUO, Z.M., Applications of a Zp index theory to periodic solutions for a class of functional differential equations, J. Math. Anal. Appl., 257 (1) (2001), 189–205