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Browsing by Subject "first order"

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  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    On the stability of first order impulsive evolution equations
    (2014) Wang, JinRong; Fečkan, Michal; Zhou, Yong
    In this paper, concepts of Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability for impulsive evolution equations are raised. Ulam-Hyers-Rassias stability results on a compact interval and an unbounded interval are presented by using an impulsive integral inequality of the Gronwall type. Two examples are also provided to illustrate our results. Finally, some extensions of the Ulam-Hyers-Rassias stability for the case with infinite impulses are given.
  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    Oscillation conditions for difference equations with several variable delays
    (Wydawnictwa AGH, 2023) El-Matary, Bassant M.; El-Morshedy, Hassan A.; Benekas, Vasileios; Stavroulakis, Ioannis P.
    A technique is developed to establish a new oscillation criterion for a first-order linear difference equation with several delays and non-negative coefficients. Our result improves recent oscillation criteria and covers the cases of monotone and non-monotone delays. Moreover, the paper is concluded with an illustrative example to show the applicability and strength of our result.