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Periodic solutions for a kind of second order differential equation with multiple deviating arguments. (English) Zbl 1037.34065

Summary: By means of a continuation theorem of coincidence degree theory, some new results on the existence, and nonexistence of periodic solutions for a kind of second-order functional-differential equation with multiple deviating arguments are obtained.

MSC:

34K13 Periodic solutions to functional-differential equations
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[1] Fonda, A.; Habets, P., Periodic solutions of asympotically positive homogeneous differential equations, J. diff. eqns., 81, 68-97, (1989) · Zbl 0692.34041
[2] Gossez, J.P.; Omari, P., Periodic solutions of a second order ordinary differential equation: a necessary and sufficient condition for nonresonance, J. diff. eqns., 94, 67-82, (1992) · Zbl 0743.34045
[3] Din, T.; Iannacci, R.; Zanolin, F., Existence and multiplicity results for periodic solutions of semilinear Duffing equations, J. diff. eqns., 105, 364-409, (1993) · Zbl 0785.34033
[4] Ge, W., On the existence of harmonic solution of Liénard systems, J. nonlinear anal., TMA, 16, 2, 183-190, (1991) · Zbl 0735.34033
[5] Wang, Z., Periodic solutions of Lie nard differential equations with subquadratic potential conditions, J. math. anal. appl., 256, 127-141, (2001) · Zbl 0980.34038
[6] Huang, X.; Xiang, Z., On the existence of 2π-periodic solutions of Duffing type equation x″(t)+g(x(t−τ))=p(t), Chin. sci. bull., 39, 1, 201-203, (1994)
[7] Layton, W., Periodic solutions of a nonlinear delay equations, J. math. anal., 77, 443-460, (1980)
[8] Ma, S.W.; Wang, Z.C.; Yu, J.S., Coincidence degree and periodic solutions of Duffing equations, Nonlinear anal., TMA, 34, 443-460, (1998) · Zbl 0931.34048
[9] Ma, S.W.; Wang, Z.C.; Yu, J.S., An abstract theorem at resonance and its applications, Diff. eqns., 145, 274-294, (1998) · Zbl 0940.34056
[10] Lu, S.; Ge, W., On the existence of periodic solutions of second order differential equations with deviating arguments, Acta. math. sinica, 45, 4, 811-818, (2002), (in Chinese) · Zbl 1027.34079
[11] Game, R.E.; Mawhin, J.L., Coincidence degree and nonlinear differential equations, (1977), Springer Berlin
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