Positive periodic solutions of state-dependent functional differential equations

Abstract

Consider the existence of positive periodic solutions of the non-autonomous state-dependent delay differential equation

with the impulses as follows

It is shown that under reasonable conditions, the equation has positive periodic solutions and under certain conditions the equation has no positive T-periodic solution.

Keywords:

• Impulses
• Functional differential equation
• Positive periodic solution
• Cone
• Fixed point theorem
• AMS Subject Classifications: 34C25
• 34K15
• 92D25

Acknowledgement

The first author was supported by the Science Foundation of Educational Committee of Hunan Province (02C369) and both authors supported by the National Natural Sciences Foundation of P.R. China (10371006).

The authors would like to thank the referees and the editorial board for several helpful comments and suggestions.