학술저널
NOTE ON SPECTRUM OF LINEAR DIFFERENTIAL OPERATORS WITH PERIODIC COEFFICIENTS
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 30, No. 3
-
2017.08323 - 329 (7 pages)
- 6
In this paper, by rigorous calculations, we consider L 2 (R)-spectrum of linear differential operators with periodic coeffi-cients. 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 Flo-quet theory, we prove rigorously that L 2 (R)-spectrum of the linear operator is determined by the eigenvalues of Floquet matrix.
1. Introduction
2. Exponential dichotomy
3. Proof of the main theorem
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