Opuscula Mathematica
Opuscula Math. 34, no. 3 (), 639-657
Opuscula Mathematica

On the stability of first order impulsive evolution equations

Abstract. 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.
Keywords: first order, impulsive evolution equations, Ulam-Hyers-Rassias stability.
Mathematics Subject Classification: 34G20, 34D10, 45N05.
Cite this article as:
JinRong Wang, Michal Fečkan, Yong Zhou, On the stability of first order impulsive evolution equations, Opuscula Math. 34, no. 3 (2014), 639-657, http://dx.doi.org/10.7494/OpMath.2014.34.3.639
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ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
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