# American Institute of Mathematical Sciences

December  2017, 6(4): 599-613. doi: 10.3934/eect.2017030

## Exact controllability results for a class of abstract nonlocal Cauchy problem with impulsive conditions

 1 Department of Mathematics, Kongunadu Arts and Science College, Coimbatore -641 029, Tamil Nadu, India 2 Department of Mathematics, SRMV College of Arts and Science, Coimbatore -641 020, Tamil Nadu, India

* Corresponding author: R. Poongodi

Received  June 2016 Revised  May 2017 Published  September 2017

This paper deals with exact controllability of a class of abstract nonlocal Cauchy problem with impulsive conditions in Banach spaces. By using Sadovskii fixed point theorem and Mönch fixed point theorem, exact controllability results are obtained without assuming the compactness and Lipschitz conditions for nonlocal functions. An example is given to illustrate the main results.

Citation: Poongodi Rathinasamy, Murugesu Rangasamy, Nirmalkumar Rajendran. Exact controllability results for a class of abstract nonlocal Cauchy problem with impulsive conditions. Evolution Equations & Control Theory, 2017, 6 (4) : 599-613. doi: 10.3934/eect.2017030
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