A Note on Asymptotic Equilibrium for Fuzzy Differential Equations

Abstract

The asymptotic equilibrium results for fuzzy differential systems $\left(GCP\right)\hspace{0.17em}{x}^{\prime }=f_1\left(t,x,y\right),y^{\prime }=f_2(t,x,y)$ are investigated, where $f_1\left(t,x,y\right)$ satisfies the compactness-type and $f_2\left(t,x,y\right)$ satisfies the dissipative-type conditions. It is worth mentioning that the uniformly continuous conditions of $f\left(t,x,y\right)$ are removed in Song et al. (2005). That is to say, the results of Song et al. (2005) are extended. In addition, the global existence and asymptotic equilibrium results of fuzzy differential systems $\left(CP\right)\hspace{0.17em}{x}^{\prime }\left(t\right)=f\left(t,x\right),x\left(0\right)=x_0$ are obtained.