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)Khayyam Journal of Mathematics2423-47885120190101On The Stability of The Quasi-Linear Implicit Equations in Hilbert Spaces1051128122210.22034/kjm.2019.81222ENMehdiBenabdallahDepartment of Mathematics, Faculty of Math and Computer, USTOran,
31000, AlgeriaMohamedHaririDepartment of Mathematics, University of Djillali Liabes, Sidi Bel-Abbes,
22000, Algeria.Journal Article20180501We 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 $$Ax'(t)=Bx(t)+theta(t,x(t)),quad tgeq 0 .$$http://www.kjm-math.org/article_81222_42e39894a1979bb86b55e195a4835a6e.pdf