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Topological Methods in Nonlinear Analysis

Periodic solutions for second order singular differential systems with parameters
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Periodic solutions for second order singular differential systems with parameters

Authors

  • Fanglei Wang
  • Jifeng Chu
  • Stefan Siegmund

DOI:

https://doi.org/10.12775/TMNA.2015.058

Keywords

Periodic solutions, second order differential systems, singular, fixed point theorem, parameter, upper and lower solutions

Abstract

In this paper we consider the existence of periodic solutions of one-parameter and two-parameter families of second order singular differential equations.

References

D. Bonheure and C. De Coster, Forced singular oscillators and the method of lower and upper solutions, Topol. Methods Nonlinear Anal. 22 (2003), 297-317.

J. Chu and P.J. Torres, Applications of Schauder's fixed point theorem to singular diifferential equations, Bull. Lond. Math. Soc. 39 (2007), 653-660.

J. Chu, P.J. Torres and M. Zhang, Periodic solutions of second order non-autonomous singular dynamical systems, J. Differential Equations 239 (2007), 196-212.

J. Chu and Z. Zhang, Periodic solutions of second order superlinear singular dynamical systems, Acta Appl. Math. 111 (2010), 179-187.

C.De. Coster and P. Habets, An overview of the method of lower and upper solutions for ODEs, Nonlinear analysis and its applications to differential equations (Lisbon, 1998), 3-22, Progr. Nonlinear Differential Equations Appl. 43, Birkhauser, Boston, Boston, MA, 2001.

D. Franco and J.R.L. Webb, Collisionless orbits of singular and nonsingular dynamical systems, Discrete Contin. Dyn. Syst. 15 (2006), 747-757.

D. Franco and P.J. Torres, Periodic solutions of singular systems without the strong force condition, Proc. Amer. Math. Soc. 136 (2008), 1229-1236.

J. R. Graef, L. Kong and H. Wang, Existence, multiplicity, and dependence on a parameter for a periodic boundary value problem, J. Differential Equations 245 (2008), 1185-1197.

D. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press, New York, 1988.

R. Hakl, P.J. Torres and M. Zamora, Periodic solutions of singular second order differential equations: upper and lower functions, Nonlinear Anal. 74 (2011), 7078-7093.

D. Jiang, J. Chu and M. Zhang, Multiplicity of positive periodic solutions to superlinear repulsive singular equations, J. Differential Equations 211 (2005), 282-302.

A. C. Lazer and S. Solimini, On periodic solutions of nonlinear differential equations with singularities, Proc. Amer. Math. Soc. 99 (1987), 109-114.

D. O'Regan and H. Wang, Positive periodic solutions of systems of second order ordinary differential equations, Positivity 10 (2006), 285-298.

R. Precup, A vector version of Krasnosel'skii's fixed point theorem in cones and poisitve periodic solutions of nonlinear systems, J. Fixed Point Theory Appl. 2 (2007), 141-151.

I. Rachunkova, M. Tvrdy and I. Vrkoc, Existence of nonnegative and nonpositive solutions for second order periodic boundary value problems, J. Differential Equations 176 (2001), 445-469.

P. J. Torres, Existence of one-signed periodic solutions of some second-order differential equations via a Krasnosel'skii fixed point theorem, J. Differential Equations 190 (2003), 643-662.

P. J. Torres, Non-collision periodic solutions of forced dynamical systems with weak singularities, Discrete Contin. Dyn. Syst. 11 (2004), 693-698.

P. J. Torres, Weak singularities may help periodic solutions to exist, J. Differential Equations 232 (2007), 277-284.

F. Wang and Y. An, Existence and multiplicity results of positive doubly periodic solutions for nonlinear telegraph system, J. Math. Anal. Appl. 349 (2009), 30-42.

H. Wang, Positive periodic solutions of functional differential equations, J. Differential Equations 202 (2004), 354-366.

H. Wang, Positive periodic solutions of singular systems with a parameter, J. Differential Equations 249 (2010), 2986-3002.

J. Wu and Z. Wang, Positive periodic solutions of second-order nonlinear differential systems with two parameters, Comput. Math. Appl. 56 (2008), 43-54.

P. Yan and M. Zhang, Higher order nonresonance for differential equations with singularities, Math. Methods Appl. Sci. 26 (2003), 1067-1074.

X. Yang, Existence of positive solutions for $2m$-order nonlinear differential systems, Nonlinear Anal. 61 (2005), 77-95.

G. Zhang and S.S. Cheng, Positive periodic solutions of coupled delay differential systems depending on two parameters, Taiwanese J. Math. 8 (2004), 639-652.

M. Zhang, Periodic solutions of equations of Ermakov-Pinney type, Adv. Nonlinear Stud. 6 (2006), 57-67.

Vol 46, No 2 (December 2015)

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Published

2015-12-01

How to Cite

1.
WANG, Fanglei, CHU, Jifeng & SIEGMUND, Stefan. Periodic solutions for second order singular differential systems with parameters. Topological Methods in Nonlinear Analysis [online]. 1 December 2015, T. 46, nr 2, s. 549–562. [accessed 6.2.2023]. DOI 10.12775/TMNA.2015.058.
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