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This paper is related to the spectral stability of traveling wave solutions of partial
differential equations. In the first part of the paper we use the Gohberg-Rouche Theorem
to prove equality of the algebraic multiplicity of an isolated eigenvalue of an abstract
operator on a Hilbert space, and the algebraic multiplicity of the eigenvalue of the
corresponding Birman-Schwinger type operator pencil. In the second part of the paper we
apply this result...
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