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• Dichotomy theorems for evolution equations ﻿

(University of Missouri--Columbia, 2008)
In the first part of this work, under minimal assumptions, we characterize the Fredholm property and compute the Fredholm index of abstract differential operators -d/dt + A([dot]) acting on spaces of functions R [arrow] ...
• The Evans function, the Weyl-Titchmarsh function, and the Birman-Schwinger operators ﻿

(University of Missouri--Columbia, 2012)
We focus on the spectral stability of travelling wave solutions of partial differential equations. First, we use the Gohberg-Rouche Theorem to prove equality of the algebraic multiplicity of an isolated eigenvalue of an ...
• Stability estimates for semigroups and partly parabolic reaction diffusion equations ﻿

(University of Missouri--Columbia, 2013)
The purpose of my dissertation is the application of the methods of abstract theory of strongly continuous operator semigroups (and of evolution semigroups in particular) to study of the spectral properties of a class of ...
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