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Existence of multiple positive periodic solutions for functional differential equations. (English) Zbl 1110.34043
Summary: By employing Krasnoselskii’s fixed-point theorem, we investigate the existence of multiple positive periodic solutions for functional-differential equations of the form \[ \dot x(t)=A(t,x(t))x(t)+\lambda f(t,x_t), \] where \(\lambda>0\) is a parameter. Some easily verifiable sufficient criteria are established.

MSC:
34K10 Boundary value problems for functional-differential equations
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[1] Chow, S.-N., Existence of periodic solutions of autonomous functional differential equations, J. differential equations, 15, 350-378, (1974) · Zbl 0295.34055
[2] Deimling, K., Nonlinear functional analysis, (1985), Springer-Verlag New York · Zbl 0559.47040
[3] Krasnoselskii, M.A., Positive solution of operator equation, (1964), Noordhoff Gröningen
[4] Jiang, D.Q.; Wei, J.J.; Zhang, B., Positive periodic solutions of functional differential equations and population models, Electron. J. differential equations, 71, 1-13, (2002)
[5] Jiang, D.Q.; O’Regan, D.; Agarwal, R.P.; Xu, X.J., On the number of positive periodic solutions of functional differential equations and population models, Math. models methods appl. sci., 15, 4, 555-573, (2005) · Zbl 1087.34046
[6] Makay, G., Periodic solutions of dissipative functional differential equations, J. tohoku math., 46, 417-426, (1994) · Zbl 0805.34059
[7] Ma, M.J.; Yu, J.S., Existence of multiple positive periodic solutions for nonlinear functional difference equations, J. math. anal. appl., 305, 483-490, (2005) · Zbl 1070.39019
[8] Peng, S.G.; Zhu, S.M., Positive periodic solutions for functional differential equations with infinite delay, Chinese ann. math. ser. A, 25, 3, 285-292, (2004), (in Chinese) · Zbl 1063.34063
[9] Wang, H.Y., Positive periodic solutions of functional differential equations, J. differential equations, 202, 354-366, (2004) · Zbl 1064.34052
[10] Ye, D.; Fan, M.; Wang, H.Y., Periodic solutions for scalar functional differential equations, Nonlinear anal., 62, 1157-1181, (2005) · Zbl 1089.34056
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