The Research Of Dynamics Behavior For Several Class Of Functional Differential Equations And Delay Differential Systems

The dynamics behavior for several class of partial functional differential equations and delay differential systems be investigated in this paper. This paper be disparted to three parts.In the first part, we give a basic summarization for the dynamics behavior for partial functional differential equations and delay differential systems. By the time, the main content of research of this paper be introduced in here.The oscillation of solutins for several class of functional differential equation be investigated in the second part. This part be arranged as follows: First, we'll consider the existence for the eventually positiove solutions for a class of higher-order functional differential equations, we obain a new condition which the eventually positive solutions existent, this condition is more sample than some references. According to the above, we study the compare oscillation for a class of higher-order functional differential equations. In the case which the eventually positive solution existent, we sort the positive solutions. Through the discussing of the oscillation of the solutions for a class of parabolic delay differential equations, we investigate the oscillation of solutions for a class of parabolic delay differential equations with positive and negative ceofficient in the farther, some errors in some references be corrected, our results extende some references largely. Using the conditions which the eventually positive solutions existent, we study the oscillation and forced oscillations for a class of higher-order parabolic delay differential system, we'll ob-tian some conditions that every solution oscillates or oscillates forcedly. A class of integral inequality be investigated in the finally, which be beneficial to the study for some delay differential equations and integral equations. By the time, we have put forward to a note for the forced oscillation for a class of higher-order delay differential system.In the part 3, the existence for the invariant set and attractor set for a class of higher-order delay differential system , a class of higher-order parabolic delay differential system and a class of dispersed higher-order delay differential system be investigated respectively, we'll estimate the range for the existence of the invariant set and attractor of those differential equations, which extend some references largely.