The Solvability And Oscillation Of Some Fuzzy Differential Equations

This paper mainly studies the oscillation and the existence of nonoscillatorysolutions of fuzzy delay differential equations (FDDEs) and studies the existence ofsolution of fuzzy iterative integral equations. We obtain some oscillation criteria ofsolutions to FDDEs and analysis the existence of nonoscillatory solutions ofFDDEs. As the promotion, the existence of solution of a special form of fuzzyiterative equations is given.This paper consists of four parts. Firstly, we briefly introduce the developmentof fuzzy differential equations (FDEs) and compare the different methods of FDEs.On the basis of this, we further summarize some recent results about the oscillatoryand nonoscillatory solutions of FDDEs.Secondly, in the study of oscillation, we first briefly present the necessarypreliminaries. Then, we give the asymptotic of nonoscillatory solutions of secondorder delay differential inclusion by contradiction. And then give the condition suchthat all the solutions of second order delay differential inclusion are oscillatory.Thus some oscillation criteria of solutions to FDDEs are obtained. Next, weanalysis the existence of nonoscillatory solutions of FDDEs. Through theapplication of variable substitution, we transform the differential inclusion to thestandard form, and then use comparative law and the Kakutani-Fan fixed pointtheorem to prove that the differential contains a nonoscillatory solution. And then, anumerical example shows the validity of the conclusions.Finally, as a promotion of the iterative equation, we study the existence ofsolution of a special form of fuzzy iterative equations. By imposing restrictions onseries of function coefficient, we construct a homeomorphism operator. Then, undercertain conditions, by applying Kakutani-Fan fixed theorem, it is shown that theset-valued operator for the iterative inclusion has a fixed point. That is, the iterativeinclusion has a solution. At last, similar to the previous chapter, we proved theoriginal fuzzy iterative integral equation has fuzzy solutions.