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New results on the periodic solutions for a kind of Rayleigh equation with two deviating arguments. (English) Zbl 1161.34345
Existence of periodic solutions for the class of equations with two deviating arguments of the form
\[ x''(t)+f(x'(t))+g_1(t,x(t-{\tau}_1(t)))+g_2(t,x(t-{\tau}_2(t)))=p(t) \]
is investigated. The main tools used by the authors are: the continuation theorem of the coincidence degree, a priori estimates, and differential inequalities, thus improving and generalizing previous results.

MSC:
34K13 Periodic solutions to functional-differential equations
47N20 Applications of operator theory to differential and integral equations
Software:
dde23
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References:
[1] Wang, G.; Cheng, S., A priori bounds for periodic solutions of a delay Rayleigh equation, Appl. math. lett., 12, 41-44, (1999) · Zbl 0980.34068
[2] Lu, S.; Ge, W., Some new results on the existence of periodic solutions to a kind of Rayleigh equation with a deviating argument, Nonlinear anal., 56, 501-514, (2004) · Zbl 1078.34048
[3] Lu, S.; Ge, W.; Zheng, Z., Periodic solutions for neutral differential equation with deviating arguments, Appl. math. comput., 152, 17-27, (2004) · Zbl 1070.34091
[4] Lu, S.; Ge, W.; Zheng, Z., A new result on the existence of periodic solutions for a kind of Rayleigh equation with a deviating argument, Acta math. sinica, 47, 299-304, (2004), (in Chinese) · Zbl 1293.34087
[5] Shampine, L.F.; Thompson, S., Solving DDEs in Matlab, Appl. numer. math., 37, 441-458, (2001) · Zbl 0983.65079
[6] Huang, X.; Xiang, Z., On existence of \(2 p\)-periodic solutions for delay Duffing equation \(x''(t) + g(t, x(t - \tau(t))) = p(t)\), Chinese sci. bull., 39, 201-203, (1994)
[7] Liu, B.; Huang, L., Periodic solutions for a kind of Rayleigh equation with a deviating argument, J. math. anal. appl., 321, 491-500, (2006) · Zbl 1103.34062
[8] Liu, B.; Huang, L., Periodic solutions for nonlinear \(n\)th order differential equations with delays, J. math. anal. appl., 313, 700-716, (2006) · Zbl 1105.34044
[9] Liu, B.; Huang, L., Periodic solutions for a class of forced Liénard-type equations, Acta math. appl. sin. engl. ser., 21, 81-92, (2005) · Zbl 1093.34020
[10] Peng, L., Periodic solutions for a kind of Rayleigh equation with two deviating arguments, J. franklin inst., 7, 676-687, (2006) · Zbl 1114.34051
[11] Gaines, R.; Mawhin, J., Coincidence degree and nonlinear differential equations, (1977), Springer-Verlag Berlin · Zbl 0339.47031
[12] Deimling, K., Nonlinear functional analysis, (1985), Springer New York · Zbl 0559.47040
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