%0 Journal Article
%T On The Stability of The Quasi-Linear Implicit Equations in Hilbert Spaces
%J Khayyam Journal of Mathematics
%I Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)
%Z 2423-4788
%A Benabdallah, Mehdi
%A Hariri, Mohamed
%D 2019
%\ 01/01/2019
%V 5
%N 1
%P 105-112
%! On The Stability of The Quasi-Linear Implicit Equations in Hilbert Spaces
%K exponential stability
%K operator theory
%K implicit equations
%R 10.22034/kjm.2019.81222
%X We use the generalized theorem of Liapounov to obtain some necessary and sufficient conditions for the stability of the stationary implicit equation $$Ax'(t)=Bx(t) ,quad tgeq 0 ,$$ 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 $$Ax'(t)=Bx(t)+theta(t,x(t)),quad tgeq 0 .$$
%U http://www.kjm-math.org/article_81222_42e39894a1979bb86b55e195a4835a6e.pdf