Stability of solutions for nonlinear nonautonomous differential-delay equations in Hilbert spaces.
On the “freezing” method for nonlinear nonautonomous systems with delay.
Stability of delay differential equations with oscillating coefficients.
Perturbations of functions of diagonalizable matrices.
Estimates for absolute values of matrix functions.
Positive solutions to a semilinear higher-order ODE on the half-line.
A bound for the spectral variation of two matrices.
Liapunov exponents for higher-order linear differential equations whose characteristic equations have variable real roots.
Positivity of the Green functions for higher order ordinary differential equations.
Stability of a time discrete perturbed dynamical systems with delay.
Nonlinear Volterra difference equations in space .
Abstract difference equations with nonlinearities having the local Lipschitz properties.
Positive periodic solutions of abstract difference equations.
Bounds for Fractional Powers of Operators in a Hilbert Space and Constants in Moment Inequalities
Mathematics Subject Classification: 47A56, 47A57,47A63 We derive bounds for the norms of the fractional powers of operators with compact Hermitian components, and operators having compact inverses in a separable Hilbert space. Moreover, for these operators, as well as for dissipative operators, the constants in the moment inequalities are established. * This research was supported by the Kamea Fund of Israel.
Norm estimates for solutions of matrix equations AX-XB=C and X-AXB=C
Let A, B and C be matrices. We consider the matrix equations Y-AYB=C and AX-XB=C. Sharp norm estimates for solutions of these equations are derived. By these estimates a bound for the distance between invariant subspaces of matrices is obtained.
Exponential stability of nonlinear non-autonomous multivariable systems
We consider nonlinear non-autonomous multivariable systems governed by differential equations with differentiable linear parts. Explicit conditions for the exponential stability are established. These conditions are formulated in terms of the norms of the derivatives and eigenvalues of the variable matrices, and certain scalar functions characterizing the nonlinearity. Moreover, an estimate for the solutions is derived. It gives us a bound for the region of attraction of the steady state....
Input-to-state stability of neutral type systems
We consider the system (ẋ(t) ≡ dx(t)/dt), where x(t) is the state, u(t) is the input, R(τ),R̃(τ) are matrix-valued functions, and F is a causal (Volterra) mapping. Such equations enable us to consider various classes of systems from the unified point of view. Explicit input-to-state stability conditions in terms of the L²-norm are derived. Our main tool is the norm estimates for the matrix resolvents, as well as estimates for fundamental solutions of the linear parts of the considered systems,...
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