Opuscula Math. 34, no. 3 (2014), 639-657

Opuscula Mathematica

On the stability of first order impulsive evolution equations

JinRong Wang
Michal Fečkan
Yong Zhou

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.

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  • JinRong Wang
  • Guizhou University, Department of Mathematics, Guiyang, Guizhou 550025, P.R. China
  • Guizhou Normal College, Guiyang, School of Mathematics and Computer Science, Guizhou 550018, P.R. China
  • Michal Fečkan
  • Comenius University, Faculty of Mathematics, Physics and Informatics, Department of Mathematical Analysis and Numerical Mathematics, Bratislava, Slovakia
  • Slovak Academy of Sciences, Mathematical Institute, Štefánikova 49, 814 73 Bratislava, Slovakia
  • Yong Zhou
  • Xiangtan University, Department of Mathematics, Xiangtan, Hunan 411105, P.R. China
  • Received: 2013-05-09.
  • Revised: 2013-09-09.
  • Accepted: 2013-09-29.
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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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