The Evans Function for Sturm–Liouville Operators on the Real Line

  • Todd Kapitula
  • Keith Promislow
Part of the Applied Mathematical Sciences book series (AMS, volume 185)


In this chapter we construct the Evans function for exponentially asymptotic differential operators on unbounded domains. While several key elements of the construction naturally carry over from the bounded domain construction, important new subtleties arise. To focus on these key issues, we restrict our attention to second-order Sturm–Liouville operators. The extension to higher-order linear operators in addressed in Chapter 10.


Eigenvalue Problem Riemann Surface Branch Point Essential Spectrum Point Spectrum 
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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Todd Kapitula
    • 1
  • Keith Promislow
    • 2
  1. 1.Department of Mathematics and StatisticsCalvin CollegeGrand RapidsUSA
  2. 2.Department of MathematicsMichigan State UniversityEast LansingUSA

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