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IMPULSIVE PERIODIC SOLUTIONS FOR SINGULAR PROBLEMS VIA VARIATIONAL METHODS

  • JUNTAO SUN (a1) and DONAL O’REGAN (a2)
Abstract
Abstract

In this paper we study impulsive periodic solutions for second-order nonautonomous singular differential equations. Our proof is based on the mountain pass theorem. Some recent results in the literature are extended.

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Corresponding author
For correspondence; e-mail: sunjuntao2008@163.com
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[1] R. P. Agarwal , D. Franco and D. O’Regan , ‘Singular boundary value problems for first and second order impulsive differential equations’, Aequationes Math. 69 (2005), 8396.

[2] R. P. Agarwal and D. O’Regan , ‘Existence criteria for singular boundary value problems with sign changing nonlinearities’, J. Differential Equations 183 (2002), 409433.

[3] R. P. Agarwal , K. Perera and D. O’Regan , ‘Multiple positive solutions of singular problems by variational methods’, Proc. Amer. Math. Soc. 134 (2005), 817824.

[4] B. Ahmad and J. J. Nieto , ‘Existence and approximation of solutions for a class of nonlinear impulsive functional differential equations with anti-periodic boundary conditions’, Nonlinear Anal. 69 (2008), 32913298.

[5] A. Boucherif and N. Daoudi-Merzagui , ‘Periodic solutions of singular nonautonomous second order differential equations’, Nonlinear Differ. Equ. Appl. 15 (2008), 147158.

[6] L. Chen and J. Sun , ‘Nonlinear boundary value problem for first-order impulsive functional differential equations’, J. Math. Anal. Appl. 318 (2006), 726741.

[7] L. Chen , C. C. Tisdell and R. Yuan , ‘On the solvability of periodic boundary value problems with impulse’, J. Math. Anal. Appl. 331 (2007), 233244.

[8] M. Choisy , J. F. Guégan and P. Rohani , ‘Dynamics of infectious deseases and pulse vaccination: teasing apart the embedded resonance effects’, Physica D 223 (2006), 2635.

[9] J. Chu , N. Fan and P. J. Torres , ‘Periodic solutions for second order singular damped differential equations’, J. Math. Anal. Appl. 388 (2012), 665675.

[11] J. Chu and J. J. Nieto , ‘Impulsive periodic solution of first-order singular differential equations’, Bull. Lond. Math. Soc. 40 (2008), 143150.

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[19] W. Li , Y. Chang and J. J. Nieto , ‘Solvability of impulsive neutral evolution differential inclusions with state-dependent delay’, Math. Comput. Modelling 49 (2009), 19201927.

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[25] I. Rachunková and M. Tvrdý , ‘Existence results for impulsive second-order periodic problems’, Nonlinear Anal. 59 (2004), 133146.

[26] J. Sun , H. Chen , J. J. Nieto and M. Otero-Novoa , ‘Multiplicity of solutions for perturbed second-order Hamiltonian systems with impulsive effects’, Nonlinear Anal. 72 (2010), 45754586.

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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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