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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:
34B15Nonlinear boundary value problems for ODE
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 · doi:10.1016/j.na.2003.06.001
[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 · doi:10.1017/S0013091503000774
[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 · doi:10.1016/S0377-0427(00)00438-6
[4]Guo, D.; Lakshmikantham, V.: Nonlinear problems in abstract cones, (1988)
[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 · doi:10.1016/S0022-247X(03)00493-1
[6]Krasnosel’skii, M.: Positive solutions of operator equations, (1964) · Zbl 0121.10604
[7]Li, Y.: Positive doubly periodic solutions of nonlinear telegraph equations, Nonlinear anal. 55, 245-254 (2003) · Zbl 1036.35020 · doi:10.1016/S0362-546X(03)00227-X
[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 · doi:10.1016/j.jmaa.2005.06.030
[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 · doi:10.1016/j.jmaa.2003.12.012
[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 · doi:10.1007/s11117-005-0021-2
[11]Torres, P.: Existence of one-signed periodic solutions of some second-order differential equations via a Krasnoselskii fixed point theorem, J. differential equations 190, 643-662 (2003) · Zbl 1032.34040 · doi:10.1016/S0022-0396(02)00152-3
[12]Wang, H.: On the number of positive solutions of nonlinear systems, J. math. Anal. appl. 281, 287-306 (2003) · Zbl 1036.34032 · doi:10.1016/S0022-247X(03)00100-8
[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 · doi:10.1016/S0022-247X(02)00538-3