Research on Periodic Solution for Some Classes of Third Order Functional Differential Equations with Delays 

Author  ShenQinRui 
Tutor  ZhouZongFu 
School  Anhui University 
Course  Basic mathematics 
Keywords  Three order functional differential solution with delays Periodic solution Coincidence degree Kset contractive operator Deviating argument 
CLC  O175 
Type  Master's thesis 
Year  2012 
Downloads  20 
Quotes  0 
Functional differential equation is a mathematical model describing the phenomenon with time delays.The functional differential equations with periodic delays represent a natural framework for mathematical modeling of many real world phenomena such as biology, economy, ecology, the population dynamic system and so on.Therefore, the researches on existence and uniqueness of periodic solutions for functional differential equations with periodic delays have practical significance.This paper mainly discusses the problems on existence and uniqueness of periodic solutions for some classes of three order functional differential equations with delays. The full text is divided into five chapters.In chapter Ⅰ, the background knowledge of the subjects relevant to this dissertation and the study of dynamic are introduced.Then, the main results of the thesis are introduced.In Chapter Ⅱ,using the theory of coincide degree,a type of third order functional differential equation with delays is considered.Some new results on the existence and uniqueness of periodic solutions are obtained.In Chapter Ⅲ,using the theory of coincide degree,on the based of the second chapter,a type of third order functional differential equation with more delays is considered.Some sufficient conditions that guarantee the existence and uniqueness of periodic solution of the equation are obtained.In Chapter IV,comparing the fourth chapter,a different research methods is used to study this equation.Specifically,using the continuation theory for Kset contractive operator,a type of third order functional differential equation with more delays is considored.The sufficient conditions for the existance of unique Tperiodic solution are obtained.In Chapter V,by using continuation theorem in coincidence degree theory, a type of third order pLaplacian Equation with a deviating argument ((φp((x(t)cx(tσ))"))’+f1(x(t))x’(t)+f2(x’(t))x"(t)+g(t, x(t), x(tτ(t)),(?)x(t+s) dm(s))=e(t) is considered.The sufficient condition for the existance of Tperiodic solution is obtained.