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2 results

  • OSCILLATION OF IMPULSIVE LINEAR DIFFERENTIAL EQUATIONS WITH DISCONTINUOUS SOLUTIONS

  • Part of
  • SIBEL DOĞRU AKGÖL
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 107 / Issue 1 / February 2023
    Published online by Cambridge University Press:
    05 May 2022, pp. 112-124
    Print publication:
    February 2023
    • Article
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  • Sufficient conditions are obtained for the oscillation of a general form of a linear second-order differential equation with discontinuous solutions. The innovations are that the impulse effects are in mixed form and the results obtained are applicable even if the impulses are small. The novelty of the results is demonstrated by presenting an example of an oscillating equation to which previous oscillation theorems fail to apply.

  • MULTIPLICITY OF SOLUTIONS FOR A FOURTH-ORDER IMPULSIVE DIFFERENTIAL EQUATION VIA VARIATIONAL METHODS

  • Part of
  • JUNTAO SUN, HAIBO CHEN, TIEJUN ZHOU
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 82 / Issue 3 / December 2010
    Published online by Cambridge University Press:
    13 October 2010, pp. 446-458
    Print publication:
    December 2010
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  • In this paper, we deal with the multiplicity of solutions for a fourth-order impulsive differential equation with a parameter. Using variational methods and a ‘three critical points’ theorem, we give some new criteria to guarantee that the impulsive problem has at least three classical solutions. An example is also given in order to illustrate the main results.