Abstract
In this chapter we begin the study of Ginzburg-Landau vortices. To begin with, we define u 1, the radially symmetric solution of the Ginzburg-Landau equation in all ℂ, and also L 1, the linearized Ginzburg-Landau operator about u 1. Next we carry out a careful study of all possible asymptotic behaviors of a solution of the homogeneous equation L 1 É = 0 both near the origin and near .. This yields a classification of all bounded solutions of L 1 É = 0 in ℂ. This study provides a key for understanding the definition of the weighted spaces we will work with in the subsequent chapters.
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© 2000 Springer Science+Business Media New York
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Pacard, F., Rivière, T. (2000). The Ginzburg-Landau Equation in ℂ. In: Linear and Nonlinear Aspects of Vortices. Progress in Nonlinear Differential Equations and Their Applications, vol 39. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1386-4_3
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DOI: https://doi.org/10.1007/978-1-4612-1386-4_3
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7125-3
Online ISBN: 978-1-4612-1386-4
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