Maximum Principles Around An Eigenvalue With Constant Eigenfunctions
(2008) Communications in Contemporary Mathematics — Vol. 10, n° 6, p. 1243-1259 (2008)
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- Abstract
- A class of linear operators L + lambda I between suitable function spaces is considered, when 0 is an eigenvalue of L with constant eigenfunctions. It is proved that L + lambda I satisfies a strong maximum principle when lambda belongs to a suitable pointed left-neighborhood of 0, and satisfies a strong uniform anti-maximum principle when lambda belongs to a suitable pointed right-neighborhood of 0. Applications are given to various types of ordinary or partial differential operators with periodic or Neumann boundary conditions.
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Campos, J., Mawhin, J., & Ortega, R. (2008). Maximum Principles Around An Eigenvalue With Constant Eigenfunctions. Communications in Contemporary Mathematics, 10(6), 1243-1259. https://doi.org/10.1142/S021919970800323X (Original work published 2008)