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Multiplicity of positive periodic solutions to second order differential equations

Published online by Cambridge University Press:  17 April 2009

Jifeng Chu
Affiliation:
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
Xiaoning Lin
Affiliation:
Department of Mathematics, Northeast Normal University, Changchun 130024, Jilin, China
Daqing Jiang
Affiliation:
Department of Mathematical Science, Florida Institute of Technology, Melbourne, FL 32901–6975, United States of America
Donal O'Regan
Affiliation:
Department of Mathematics, Northeast Normal University, Changchun 130024, Jilin, China
R. P. Agarwal
Affiliation:
Department of Mathematics, National University of Ireland, Galway, Ireland
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Extract

In this paper, we study the existence of positive periodic solutions to the equation x = f (t, x). It is proved that such a equation has more than one positive periodic solution when the nonlinearity changes sign. The proof relies on a fixed point theorem in cones.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2006

References

[1]Lazer, A.C. and Solimini, S., ‘On periodic solutions of nonlinear differential equations with singularities’, Proc. Amer. Math. Soc. 99 (1987), 109114.CrossRefGoogle Scholar
[2]Rachunková, I., Tvrdý, M. and Vrkoč, I., ‘Existence of nonnegative and nonpositive solutions for second order periodic boundary value problems’, J. Differential Equations 176 (2001), 445469.CrossRefGoogle Scholar
[3]Zhang, M.R., ‘A relationship between the periodic and the Dirichlet BVPs of singular differential equations’, Proc. Roy. Soc. Edinburgh Sect. A 128 (1998), 10991114.CrossRefGoogle Scholar
[4]De Coster, C. and Habets, P., ‘Upper and lower solutions in the theory of ODE boundary value problems: classical and recent results’, in Nonlinear Analysis and Boundary Value Problems for Ordinary Differential Equations, CISM-ICMS 371, (Zano-lin, F., Editor) (Springer-Verlag, New York, 1996), pp. 178.Google Scholar
[5]Mawhin, J., ‘Topological degree and boundary value problems for nonlinear differential equations’, in Topological Methods for Ordinary Differential Equations, (Furi, M. and Zecca, P., Editors), Lecture Notes Math. 1537 (Springer-Verlag, New York, Berlin, 1993), pp. 74142.CrossRefGoogle Scholar
[6]Erbe, L.H. and Mathsen, R.M., ‘Positive solutions for singular nonlinear boundary value problems’, Nonlinear Anal. 46 (2001), 979986.CrossRefGoogle Scholar
[7]Torres, P.J., ‘Existence of one-signed periodic solutions of some second-order differential equations via a Krasnoselskii fixed point theorem’, J. Differential Equations 190 (2003), 643662.CrossRefGoogle Scholar
[8]Deimling, K., Nonlinear functional analysis (Springer-Verlag, Berlin, 1985).CrossRefGoogle Scholar
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