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International Journal of Nonlinear Sciences and Numerical Simulation

Editor-in-Chief: Birnir, Björn

Editorial Board: Armbruster, Dieter / Chen, Xi / Bessaih, Hakima / Chou, Tom / Grauer, Rainer / Marzocchella, Antonio / Rangarajan, Govindan / Trivisa, Konstantina / Weikard, Rudi

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Volume 19, Issue 7-8


Existence and Uniqueness of Classical and Mild Solutions of Generalized Impulsive Evolution Equation

Vishant Shah
  • Department of Applied Mathematics, Faculty of Technology and Engineering, The M. S. University of Baroda, Vadodara, India
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  • Department of Applied Mathematics, Faculty of Technology and Engineering, The M. S. University of Baroda, Vadodara, India
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Published Online: 2018-10-25 | DOI: https://doi.org/10.1515/ijnsns-2018-0042


In this article, the existence and uniqueness of generalized nonlinear impulsive evolution equation is derived. The proposed system is modeled with nonlinear perturbed force which changes after every impulse. The Banach contraction principle is applied to prove the existence and uniqueness of mild solution. The existence and uniqueness of classical solution is obtained by fixing the impulse and the conditions in which mild solution becomes classical solution also obtained. Finally an example is illustrated to the effectiveness of main results.

Keywords: semigroup; differential equations; impulsive conditions; classical solution; mild solution

MSC 2010: 34A37; 34G20; 34G60


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About the article

Received: 2018-02-19

Accepted: 2018-10-02

Published Online: 2018-10-25

Published in Print: 2018-12-19

Citation Information: International Journal of Nonlinear Sciences and Numerical Simulation, Volume 19, Issue 7-8, Pages 775–780, ISSN (Online) 2191-0294, ISSN (Print) 1565-1339, DOI: https://doi.org/10.1515/ijnsns-2018-0042.

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