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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 968541, 5 pages
Existence of Periodic Solutions to Multidelay Functional Differential Equations of Second Order
Department of Mathematics, Faculty of Sciences, Yüzüncü Yıl University, 65080 Van, Turkey
Received 23 August 2013; Accepted 3 October 2013
Academic Editor: S. A. Mohiuddine
Copyright © 2013 Cemil Tunç and Ramazan Yazgan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- R. E. Gaines and J. L. Mawhin, Coincidence Degree, and Nonlinear Differential Equations, vol. 568 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1977.
- T. Yoshizawa, “Stability theory by Liapunov's second method,” Publications of the Mathematical Society of Japan 9, The Mathematical Society of Japan, Tokyo, Japan, 1966.
- J. M. Zhao, K. L. Huang, and Q. S. Lu, “The existence of periodic solutions for a class of functional-differential equations and their application,” Applied Mathematics and Mechanics. English Edition, vol. 15, no. 1, pp. 49–59, 1994, translated from Applied Mathematics and Mechanics, vol. 15, no. 1, pp. 49–58, 1994.
- T. A. Burton, Stability and Periodic Solutions of Ordinary and Functional Differential Equations, Dover, Mineola, NY, USA, 2005, Corrected Version of the 1985 Original.
- S. Ahmad and M. R. Rao, Theory of Ordinary differential Equations. With Applications in Biology and Engineering, Affiliated East-West Press, New Delhi, India, 1999.
- A. Constantin, “A note on a second-order nonlinear differential system,” Glasgow Mathematical Journal, vol. 42, no. 2, pp. 195–199, 2000.
- J. R. Graef, “On the generalized Liénard equation with negative damping,” Journal of Differential Equations, vol. 12, pp. 34–62, 1972.
- L. H. Huang and J. S. Yu, “On boundedness of solutions of generalized Liénard's system and its application,” Annals of Differential Equations, vol. 9, no. 3, pp. 311–318, 1993.
- Z. Jin, “Boundedness and convergence of solutions of a second-order nonlinear differential system,” Journal of Mathematical Analysis and Applications, vol. 256, no. 2, pp. 360–374, 2001.
- B. Liu and L. Huang, “Boundedness of solutions for a class of retarded Liénard equation,” Journal of Mathematical Analysis and Applications, vol. 286, no. 2, pp. 422–434, 2003.
- J. E. Nápoles Valdés, “Boundedness and global asymptotic stability of the forced Liénard equation,” Revista de la Unión Matemática Argentina, vol. 41, no. 4, pp. 47–59, 2000.
- C. X. Qian, “Boundedness and asymptotic behaviour of solutions of a second-order nonlinear system,” The Bulletin of the London Mathematical Society, vol. 24, no. 3, pp. 281–288, 1992.
- C. Tunç, “A note on the bounded solutions,” Applied Mathematics and Information Sciences, vol. 8, no. 1, pp. 393–399, 2014.
- C. Tunç, “A note on boundedness of solutions to a class of non-autonomous differential equations of second order,” Applicable Analysis and Discrete Mathematics, vol. 4, no. 2, pp. 361–372, 2010.
- C. Tunç, “Boundedness results for solutions of certain nonlinear differential equations of second order,” Journal of the Indonesian Mathematical Society, vol. 16, no. 2, pp. 115–126, 2010.
- C. Tunç, “Uniformly stability and boundedness of solutions of second order nonlinear delay differential equations,” Applied and Computational Mathematics, vol. 10, no. 3, pp. 449–462, 2011.
- C. Tunç, “On the boundedness of solutions of a non-autonomous differential equation of second order,” Sarajevo Journal of Mathematics, vol. 7(19), no. 1, pp. 19–29, 2011.
- C. Tunç, “Stability and uniform boundedness results for non-autonomous Lienard-type equations with a variable deviating argument,” Acta Mathematica Vietnamica, vol. 37, no. 3, pp. 311–325, 2012.
- C. Tunç, “On the stability and boundedness of solutions of a class of nonautonomous differential equations of second order with multiple deviating arguments,” Afrika Matematika, vol. 23, no. 2, pp. 249–259, 2012.
- C. Tunç, “Stability to vector Lienard equation with constant deviating argument,” Nonlinear Dynamics, vol. 73, no. 3, pp. 1245–1251, 2013.
- C. Tunç, “New results on the existence of periodic solutions for Rayleigh equation with state-dependent delay,” Journal of Mathematical and Fundamental Sciences, vol. 45, no. 2, pp. 154–162, 2013.
- C. Tunç and E. Tunç, “On the asymptotic behavior of solutions of certain second-order differential equations,” Journal of the Franklin Institute, vol. 344, no. 5, pp. 391–398, 2007.
- J. Zhou, “Necessary and sufficient conditions for boundedness and convergence of a second-order nonlinear differential system,” Acta Mathematica Sinica. Chinese Series, vol. 43, no. 3, pp. 415–420, 2000.