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

Document Type : Original Article


1 Department of Mathematics, Faculty of Math and Computer, USTOran, 31000, Algeria

2 Department of Mathematics, University of Djillali Liabes, Sidi Bel-Abbes, 22000, Algeria.


We use the generalized theorem of Liapounov to obtain some necessary and sufficient conditions for the stability of the stationary implicit equation $$Ax'(t)=Bx(t) ,\quad t\geq 0 ,$$ 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 $$Ax'(t)=Bx(t)+\theta(t,x(t)),\quad t\geq 0 .$$


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