Explicit stability conditions for integro-differential equations with operator coefficients

New explicit stability conditions are derived for integro-differential equations with operator coefficients which arise in viscoelasticity. Unlike previous studies, the coefficients are not assumed to be self-adjoint and commuting operators. Our stability conditions are formulated in terms of norms of the operator coefficients and some auxiliary operators, as well as two specific characteristics of kernels of the integral operators. The conditions developed are applied to determine the ultimate flow velocity in the flutter problem for a viscoelastic panel in supersonic gas flow. The effect of the material viscosity on the critical gas velocity is analysed numerically.