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 $$Ax'(t)=Bx(t) ,quad tgeq 0 ,$$ 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 $$Ax'(t)=Bx(t)+theta(t,x(t)),quad tgeq 0 .$$
UR - http://www.kjm-math.org/article_81222.html
L1 - http://www.kjm-math.org/article_81222_42e39894a1979bb86b55e195a4835a6e.pdf
ER -