On The Stability of The Quasi-Linear Implicit Equations in Hilbert Spaces

[摘要] We use the generalized theorem of Liapounov to obtain some necessary and sufficient conditions for the stability of the stationary implicit equation Ax0 (t) = Bx(t), t ≥ 0, where A and B are bounded operators in Hilbert spaces. The achieved results can be applied to the stability for the quasi-linear implicit equation Ax0 (t) = Bx(t) + θ(t, x(t)), t ≥ 0.

[学科分类] 公共、环境与职业健康