@article {
author = {Benabdallah, Mehdi and Hariri, Mohamed},
title = {On The Stability of The Quasi-Linear Implicit Equations in Hilbert Spaces},
journal = {Khayyam Journal of Mathematics},
volume = {5},
number = {1},
pages = {105-112},
year = {2019},
publisher = {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)},
issn = {2423-4788},
eissn = {2423-4788},
doi = {10.22034/kjm.2019.81222},
abstract = {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 $$Ax'(t)=Bx(t)+\theta(t,x(t)),\quad t\geq 0 .$$},
keywords = {exponential stability,operator theory,implicit equations},
url = {http://www.kjm-math.org/article_81222.html},
eprint = {http://www.kjm-math.org/article_81222_42e39894a1979bb86b55e195a4835a6e.pdf}
}