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3 results

  • THREE POSITIVE PERIODIC SOLUTIONS FOR DYNAMIC EQUATIONS WITH PIECEWISE CONSTANT ARGUMENT AND IMPULSE ON TIME SCALES*

  • YONGKUN LI, ERLIANG XU
  • Journal:
    Glasgow Mathematical Journal / Volume 53 / Issue 2 / May 2011
    Published online by Cambridge University Press:
    08 December 2010, pp. 369-377
    Print publication:
    May 2011
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  • In this paper, by using the Leggett–Williams fixed point theorem, the existence of three positive periodic solutions for differential equations with piecewise constant argument and impulse on time scales is investigated. Some easily verifiable sufficient criteria are established. Finally, an example is given to illustrate the results.

  • Almost Periodicity and Lyapunov's Functions for Impulsive Functional Differential Equations with Infinite Delays

  • Gani Tr. Stamov
  • Journal:
    Canadian Mathematical Bulletin / Volume 53 / Issue 2 / 01 June 2010
    Published online by Cambridge University Press:
    20 November 2018, pp. 367-377
    Print publication:
    01 June 2010
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  • This paper studies the existence and uniqueness of almost periodic solutions of nonlinear impulsive functional differential equations with infinite delay. The results obtained are based on the Lyapunov–Razumikhin method and on differential inequalities for piecewise continuous functions.

  • BOUNDEDNESS OF IMPULSIVE FUNCTIONAL DIFFERENTIAL EQUATIONS WITH VARIABLE IMPULSIVE PERTURBATIONS

  • Part of
  • I. M. Stamova
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 77 / Issue 2 / April 2008
    Published online by Cambridge University Press:
    01 April 2008, pp. 331-345
    Print publication:
    April 2008
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  • In the present paper an initial value problem for impulsive functional differential equations with variable impulsive perturbations is considered. By means of piecewise continuous functions coupled with the Razumikhin technique, sufficient conditions for boundedness of solutions of such equations are found.