Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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NOTE ON SPECTRUM OF LINEAR DIFFERENTIAL OPERATORS WITH PERIODIC COEFFICIENTS

  • Jung, Soyeun (Division of International Studies Kongju National University)
  • Received : 2017.03.27
  • Accepted : 2017.04.28
  • Published : 2017.08.15
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Abstract

In this paper, by rigorous calculations, we consider $L^2({\mathbb{R}})-spectrum$ of linear differential operators with periodic coefficients. These operators are usually seen in linearization of nonlinear partial differential equations about spatially periodic traveling wave solutions. Here, by using the solution operator obtained from Floquet theory, we prove rigorously that $L^2({\mathbb{R}})-spectrum$ of the linear operator is determined by the eigenvalues of Floquet matrix.

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References

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