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Multiple positive solutions to superlinear periodic boundary value problems with repulsive singular forces. (English) Zbl 1042.34047

The authors prove the existence of one or two periodic solutions to a superlinear equation having a singularity of repulsive type.

MSC:

34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
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References:

[1] Gordon, W., Conservative dynamical systems involving strong forces, Trans. amer. math. soc., 204, 113-135, (1975) · Zbl 0276.58005
[2] Majer, P.; Terracini, S., Periodic solutions to some problems of n-body type, Arch. rational mech. anal., 124, 381-404, (1993) · Zbl 0782.70010
[3] Zhang, S., Multiple closed orbits of fixed energy for N-body-type problems with gravitational potentials, J. math. anal. appl., 208, 462-475, (1997) · Zbl 0880.70008
[4] Wang, J.; Jiang, D.Q., A singular nonlinear second-order periodic boundary value problem, TĂ´hoku math. J., 50, 203-210, (1998) · Zbl 0916.34027
[5] Fonda, A.; Manasevich, R.F.; Zanolin, F., Subharmonic solutions for some second order differential equations with singularities, SIAM J. math. anal., 24, 1294-1311, (1993) · Zbl 0787.34035
[6] del Pino, M.A.; Manasevich, R.F., Infinitely many T-periodic solutions for a problem arising in nonlinear elasticity, J. differential equations, 103, 260-277, (1993) · Zbl 0781.34032
[7] del Pino, M.A.; Manasevich, R.F.; Montero, A., T-periodic solutions for some second-order differential equations with singularities, Proc. roy. soc. Edinburgh sect. A, 120, 231-243, (1992) · Zbl 0761.34031
[8] Zhang, M.R., A relationship between the periodic and the Dirichlet BVPs of singular differential equations, Proc. roy. soc. Edinburgh sect. A, 128, 1099-1114, (1998) · Zbl 0918.34025
[9] Zhang, M.R., Periodic solutions of lienard equations with singular forces of repulsive type, J. math. anal. appl., 203, 254-269, (1996) · Zbl 0863.34039
[10] Deimling, K., Nonlinear functional analysis, (1985), Springer Berlin · Zbl 0559.47040
[11] Jiang, D.Q., On the existence of positive solutions to second order periodic BVPs, Acta math. sinica, 18, 31-35, (1998)
[12] O’Regan, D., Existence theory for nonlinear ordinary differential equations, (1997), Kluwer Academic Dordrecht · Zbl 1077.34505
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