We contribute to the perturbation theory of nonlinear eigenvalue problems in three ways. First, we extend the formula for the sensitivity of a simple eigenvalue with respect to a variation of a parameter to the case o...
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We contribute to the perturbation theory of nonlinear eigenvalue problems in three ways. First, we extend the formula for the sensitivity of a simple eigenvalue with respect to a variation of a parameter to the case of multiple nonsemisimple eigenvalues, thereby providing an explicit expression for the leading coefficients of the Puiseux series of the emanating branches of eigenvalues. Second, for a broad class of delay eigenvalue problems, the connection between the finitedimensional nonlinear eigenvalue problem and an associated infinite-dimensional linear eigenvalue problem is emphasized in the developed perturbation theory. Finally, in contrast to existing work on analyzing multiple eigenvalues of delay systems, we develop all theory in a matrix framework, i.e., without reduction of a problem to the analysis of a scalar characteristic quasi-polynomial.
Exact solutions of the linear water-wave problem describing oblique water waves trapped by a submerged horizontal cylinder of small (but otherwise fairly arbitrary) cross-section in a two-layer fluid are constructed i...
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Exact solutions of the linear water-wave problem describing oblique water waves trapped by a submerged horizontal cylinder of small (but otherwise fairly arbitrary) cross-section in a two-layer fluid are constructed in the form of convergent series in powers of the small parameter characterising the "thinness" of the cylinder. The terms of this series are expressed through the solutions of the exterior Neumann problem for the Laplace equation describing the flow of unbounded fluid past the cylinder.
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