Asymptotic equilibrium and stability of fuzzy differential equations. (English) Zbl 1084.34052

The authors consider the asymptotic equilibrium of the following fuzzy differential equation \[ x'= f(t,x),\quad x(t_0)= x_0, \] with \(f\in C[J\times E^n, E^n]\), \(J= [t,\infty]\), \(x_0\in E^n\).
Moreover, they prove the asymptotic stability of the perturbed fuzzy differential equation \[ x'= A(t)x+ f(t,x),\quad x(t_0)= x_0, \] where \(f\in C[\mathbb{R}_+\times E^n, E^n]\), and for each \(t\in \mathbb{R}_+\), \(A(t): E^n\to E^n\) is a semilinear operator, by using Lyapunov’s direct method.
An example is discussed, too.


34D20 Stability of solutions to ordinary differential equations
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34G25 Evolution inclusions
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