Tran Thi Loan
Ukr. Mat. Zh. - 2008. - 60, № 10. - pp. 1401–1413
In this paper, the global exponential stability of a class of neural networks is investigated. The neural networks contain variable and unbounded delays. By constructing a suitable Lyapunov function and using the technique of matrix analysis, we obtain some new sufficient conditions for global exponential stability.
On the Asymptotic Behavior of Solutions of the First Initial Boundary-Value Problems for Parabolic Equations
Ukr. Mat. Zh. - 2003. - 55, № 8. - pp. 1143-1152
We consider the first initial boundary-value problem for a strongly parabolic system on an infinite cylinder with nonsmooth boundary. We prove some results on the existence, uniqueness, and asymptotic behavior of solutions as t → ∞.
On the Stability of Semilinear Nonautonomous Evolution Equations in Banach Spaces and Its Application to Strongly Parabolic Equations
Ukr. Mat. Zh. - 2002. - 54, № 12. - pp. 1714-1719
The paper is concerned with the exponential stability of the zero solution of strongly nonautonomous parabolic equations. Conditions are found on time-dependent coefficients of a parabolic equation under which its solutions converge exponentially to 0 as t → ∞.
Ukr. Mat. Zh. - 1999. - 51, № 10. - pp. 1417–1424
A sufficient condition of exponential stability of regular linear systems with bifurcation on a Banach space is proved.