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Русская версия

**S. Balamuralitharan**

Faculty of Engineering and Technology, Department of Mathematics,

SRM University, Kattankulathur - 603 203,Tamil Nadu, INDIA.

The purpose of this paper is to study the periodic solution of a certain class of third and fourth order delay differential equation impulses with Fredholm operator of index zero. We obtain the existence of periodic solution and Mawhin’s continuation theorem. The delay conditions for the Schwarz inequality of the periodic solutions are also obtained.An example is also furnished which demonstrates validity of main result. We establish some new sufficient conditions which ensure that every solution of this equation impulses to at least one periodic solution.

- Fredholm operator of index zero
- impulses
- Mawhin's continuation theorem
- periodic solutions
- third and fourth order delay differential equations

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