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Existence, multiplicity, and dependence on a parameter for a periodic boundary value problem. (English) Zbl 1203.34028

The authors discuss existence and multiplicity for a periodic boundary value problem. Krasnoselskii fixed point theorem in a cone is used in the analysis.

MSC:

34B15 Nonlinear boundary value problems for ordinary differential equations
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References:

[1] Agarwal, R. P.; O’Regan, D.; Staněk, S., Singular Lidstone boundary value problems with given maximum values for solutions, Nonlinear Anal., 55, 859-881 (2003) · Zbl 1055.34040
[2] Agarwal, R. P.; O’Regan, D.; Staněk, S., Solvability of singular Dirichlet boundary-value problems with given maximum values for positive solutions, Proc. Edinburgh Math. Soc., 48, 1-19 (2005) · Zbl 1066.34017
[3] 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, 341-356 (2001) · Zbl 0993.34022
[4] Guo, D.; Lakshmikantham, V., Nonlinear Problems in Abstract Cones (1988), Academic Press: Academic Press Orlando, FL · Zbl 0661.47045
[5] Jiang, D.; Chu, J.; O’Regan, D.; Agarwal, R., Multiple positive solutions to superlinear periodic boundary value problems with repulsive singular forces, J. Math. Anal. Appl., 286, 563-576 (2003) · Zbl 1042.34047
[6] Krasnosel’skii, M., Positive Solutions of Operator Equations (1964), Noordhoff: Noordhoff Groningen · Zbl 0121.10604
[7] Li, Y., Positive doubly periodic solutions of nonlinear telegraph equations, Nonlinear Anal., 55, 245-254 (2003) · Zbl 1036.35020
[8] Li, W.; Liu, X., Eigenvalue problems for second-order nonlinear dynamic equations on time scales, J. Math. Anal. Appl., 318, 578-592 (2006) · Zbl 1099.34026
[9] Liu, X.; Li, W., Existence and uniqueness of positive periodic solutions of functional differential equations, J. Math. Anal. Appl., 293, 28-39 (2004) · Zbl 1057.34094
[10] O’Regan, D.; Wang, H., Positive periodic solutions of systems of second order ordinary differential equations, Positivity, 10, 285-298 (2006) · Zbl 1103.34027
[11] Torres, P., Existence of one-signed periodic solutions of some second-order differential equations via a Krasnosel’skii fixed point theorem, J. Differential Equations, 190, 643-662 (2003) · Zbl 1032.34040
[12] Wang, H., On the number of positive solutions of nonlinear systems, J. Math. Anal. Appl., 281, 287-306 (2003) · Zbl 1036.34032
[13] 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, 99-107 (2003) · Zbl 1030.34024
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