TY - JOUR ID - 81222 TI - On The Stability of The Quasi-Linear Implicit Equations in Hilbert Spaces JO - Khayyam Journal of Mathematics JA - KJM LA - en SN - AU - Benabdallah, Mehdi AU - Hariri, Mohamed AD - Department of Mathematics, Faculty of Math and Computer, USTOran, 31000, Algeria AD - Department of Mathematics, University of Djillali Liabes, Sidi Bel-Abbes, 22000, Algeria. Y1 - 2019 PY - 2019 VL - 5 IS - 1 SP - 105 EP - 112 KW - exponential stability KW - operator theory KW - implicit equations DO - 10.22034/kjm.2019.81222 N2 - 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 $$Ax'(t)=Bx(t)+\theta(t,x(t)),\quad t\geq 0 .$$ UR - https://www.kjm-math.org/article_81222.html L1 - https://www.kjm-math.org/article_81222_42e39894a1979bb86b55e195a4835a6e.pdf ER -