The stability of a basic stationary motion is investigated. The problem is posed as an initial boundary-value problem of partial differential equations in the perturbations. The spectral representation of the Green’s function matrix for the linearized problem is obtained and employed to generate a generalized energy function which is then used for the stability investigation of linearized and certain nonlinear problems. The results are applied to the stability of linearized aerodynamic panel flutter problem and to a nonlinear equation with conic nonlinearity.

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