## Research

### Introduction

Our main research is to construct qualitative theory of delay equations. In the classical ordinary differential equations, the rate of change of state depends only on present time. But, it has been recognized in the field of engineering and mathematical biology that to model some phenomena more realistically, it is natural that the rate of change of state depends on past time as well as on present time. So, ordinary differential equations that take account of the effect of past state have been investigated by many mathematicians in the last half century. We are also interested in difference equations and integral equations with finite or infinite delay.

### Keyword

- Delay equation
- Stability theory
- Formal adjoint theory
- Center manifold theory

### Research Grants (Leader)

- 2019-2022, JSPS KAKENHI Grant-in-Aid for Scientific Research (C)
- 2014-2017, JSPS KAKENHI Grant-in-Aid for Scientific Research (C)
- 2009-2011, JSPS KAKENHI Grant-in-Aid for Young Scientists (B)
- 2007-2008, JSPS KAKENHI Grant-in-Aid for Young Scientists (B)
- 2006, Basic Science Research Projects of the Sumitomo Foundation
- 2003-2005, JSPS KAKENHI Grant-in-Aid for Young Scientists (B)
- 2002, Sasakawa Grants for Science Fellows of the Japan Science Society