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Article

Keywords:
Rayleigh equations; positive periodic solution; a priori estimate
Summary:
The existence of positive periodic solutions for a kind of Rayleigh equation with a deviating argument $$ x''(t)+ f(x'(t))+ g(t,x(t-\tau (t)))= p(t) $$ is studied. Using the coincidence degree theory, some sufficient conditions on the existence of positive periodic solutions are obtained.
References:
[1] Atici, F. M., Guseinov, G. Sh.: On the existence of positive solutions for nonlinear differential equations with periodic boundary conditions. J. Comput. Appl. Math. 132 (2001), 341-356. DOI 10.1016/S0377-0427(00)00438-6 | MR 1840633 | Zbl 0993.34022
[2] Gaines, R. E., Mawhin, J. L.: Coincidence Degree and Nonlinear Differential Equations. Lecture Notes in Mathematics, No. 568. Springer Berlin-Heidelberg-New York (1977). MR 0637067
[3] Jiang, D., Chu, J., Zhang, M.: Multiplicity of positive periodic solutions to superlinear repulsive singular equations. J. Differ. Equations 211 (2005), 282-302. DOI 10.1016/j.jde.2004.10.031 | MR 2125544 | Zbl 1074.34048
[4] Li, F., Liang, Z.: Existence of positive periodic solutions to nonlinear second order differential equations. Appl. Math. Lett. 18 (2005), 1256-1264. DOI 10.1016/j.aml.2005.02.014 | MR 2170881 | Zbl 1088.34038
[5] Lin, X., Li, X., Jiang, D.: Positive solutions to superlinear semipositone periodic boundary value problems with repulsive weak singular forces. Comput. Math. Appl. 51 (2006), 507-514. DOI 10.1016/j.camwa.2005.08.030 | MR 2207437 | Zbl 1105.34306
[6] Mawhin, J., Willem, M.: Critical Point Theory and Hamiltonian Systems. Springer New York (1989). MR 0982267 | Zbl 0676.58017
[7] Yang, X.: Multiple positive solutions of second-order differential equations. Nonlinear Anal., Theory Methods Appl. 62 (2005), 107-116. DOI 10.1016/j.na.2005.03.013 | MR 2139358 | Zbl 1077.34025
[8] Zhang, Z., Wang, J.: On existence and multiplicity of positive solutions to periodic boundary value problems for singular nonlinear second order differential equations. J. Math. Anal. Appl. 281 (2003), 99-107. DOI 10.1016/S0022-247X(02)00538-3 | MR 1980077 | Zbl 1030.34024
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