## Stability of solutions for nonlinear nonautonomous differential-delay equations in Hilbert spaces.(English)Zbl 1027.34083

In a real separable Hilbert space the functional-differential equation $\dot{u}+Au+B\int_{0}^{h}u(t-\tau) d\mu(\tau)=F(t,u(\cdot)),\quad t>0,$ where $$F(t,u(\cdot))$$ is a nonlinear Volterra-type operator, is considered. Estimates on the solutions are obtained. Explicit conditions for the absolute stability, and input-output stability of the zero solution are established.

### MSC:

 34K20 Stability theory of functional-differential equations 34K12 Growth, boundedness, comparison of solutions to functional-differential equations 34K30 Functional-differential equations in abstract spaces
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