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We consider two-point non-self-adjoint boundary eigenvalue problems forlinear matrix differential operators. The coefficient matrices in thedifferential expressions and the matrix boundary conditions are assumed todepend analytically on the complex spectral parameter and on the vector of realphysical parameters. We study perturbations of semi-simple multiple eigenvaluesas well as perturbations of non-derogatory eigenvalues under small variationsof the parameters. Explicit formulae describing the bifurcation of theeigenvalues are derived. Application to the problem of excitation of unstablemodes in rotating continua such as spherically symmetric MHD alpha2-dynamo andcircular string demonstrates the efficiency and applicability of the theory.

Perturbation of multiparameter non-self-adjoint boundary eigenvalue problems for operator matrices