Asymptotic equilibrium and stability of fuzzy differential equations

The local existence and uniqueness theorems and the global existence of solutions were investigated in [1–3], respectively, for the Cauchy problem of fuzzy-valued functions of a real variable whose values are in the fuzzy number space (En, D). In this paper, we first study the asymptotic equilibrium for fuzzy evolution equations. Then, the stability properties of the trivial fuzzy solution of the perturbed semilinear fuzzy evolution equations are investigated by extending the Lyapunovʹs direct method.