2010

Gecikme Argümentli Rayleigh Tipi Denklem için Periyodik Çözümlerin Varlığı Üzerine

Bu çalışmada,                  , , 0 t f t t t g t t t t t              formundaki gecikme argümentli Rayleigh tipi denklem ele alınmaktadır. Bu denklemin T-periyodik çözümlerinin varlığı üzerine yeni sonuçlar elde edilmektedir. Bu sonuçlar elde edilirken örtüşen derece teorisi kullanılmaktadır.

On The Existence of Periodic Solutions For Rayleigh-Type Equation With a Deviating Argument

In this paper, we discusse Rayleigh-type equation with a deviating argument of the form                  , , 0. t f t t t g t t t t t              New results are obtained on the existence of T-periodic solutions for this equation. In order to obtain these results, the coincidence degree is used.

PDF

___

Acan, O., 2016. Existence and uniqueness of periodic solutions for a kind of forced rayleigh equation, Gazi University Journal of Science, 29, 645-650.
Burton T. A., 1985. Stability and Periodic Solutions of Ordinary and Functional Differential Equations, Academic Press, Orland, FL
Deimling, K., 1985. Nonlinear Functional Analysis, Springer, Berlin.
Degla, G., 1997. Degree theory for compact displacements of the identity and applications, International Center for Theoretical Physics, P.O. Box 586, Italy.
Gaines, R. E., Mawhin, J., 1977. Coincidence Degree and Nonlinear Differential Equations, in: Lecture Notes in Mathematics, Springer-Verlag, Berlin, New York.
Huang, C., He, Y., Huang, L., Tan, W., 2007. New results on the periodic solutions for a kind of Rayleigh equation with two deviating arguments, Mathematical and Computer Modelling, 46, 5-6.
Li, Y., Huang, L., 2008. New results of periodic solutions for forced Rayleigh-type equations, Journal of mathematical analysis and applications, 221(1), 98105.
Liang, R., 2012. Existence and uniqueness of periodic solution for forced Rayleigh type equations, Journal of Applied Mathematics and Computing, 40, 415-425.
Liu, B., 2008. Existence and uniqueness of periodic solutions for a kind of Rayleigh equation with two deviating arguments, Computers & Mathematics with Applications, 55, 2108-2117.
Liu, B., 2009. Anti-periodic solutions for forced Rayleightype equations, Nonlinear Analaysis, 10, 2850-2856.
Liu, B., Huang, L., 2006. Periodic solutions for a kind of Rayleigh equation with a deviating argument, Journal of mathematical analysis and applications, 321, 491500.
Lu, S., Ge, W., 2004a. Periodic solutions for a kind of Liénard equations with deviating arguments, Journal of mathematical analysis and applications, 249, 231243.
Lu, S., Ge, W., 2004b. Some new results on the existence of periodic solutions to a kind of Rayleigh equation with a deviating argument, Nonlinear Analaysis, 56, 501-504
Lu, S., Ge, W., Zheng, Z., 2004. Periodic Solutions for a Kind of Rayleigh Equation with a Deviating Argument, Applied mathematics letters, 17, 443-449.
Peng, L., Liu, B., Zhou, Q., Huang, L., 2006. Periodic solutions for a kind of Rayleigh equation with two deviating arguments, Journal of the Franklin Institute, 343, 676-687.
Wang, L., Shao, J., 2010. New results of periodic solutions for a kind of forced Rayleigh-type equations, Nonlinear Analaysis, 11, 99-105.
Xiong, W., Zhou, Q., Xiao, B., Wang, Y., Long, F., 2007. Periodic solutions for a kind of Liénard equation with two deviating arguments, Nonlinear Analaysis, 8(3), 787-796.
Yu, Y., Shao, J., Yue, G., 2009. Existence and uniqueness of anti-periodic solutions for a kind of Rayleigh equation with two deviating arguments, Nonlinear Analaysis, 71, 4689-4695.
Zhou, Y., Tang, X., 2007a. On existence of periodic solutions of Rayleigh equation of retarded type, Journal of computational and applied mathematics, 203, 1-5.
Zhou, Y., Tang, X., 2007b. Periodic solutions for a kind of Rayleigh equation with a deviating argument, Computers & Mathematics with Applications, 53, 825830.
Zhou, Y., Tang, X., 2008. On existence of periodic solutions of a kind of Rayleigh equation with a deviating argument, Nonlinear Analaysis, 69, 23552361.