MAXIMUM PRINCIPLES AROUND AN EIGENVALUE WITH CONSTANT EIGENFUNCTIONS
Juan Manuel Campos, Jean L. Mawhin, Rafael Ortega · Communications in Contemporary Mathematics · 2008
A class of linear operators L + λI between suitable function spaces is considered, when 0 is an eigenvalue of L with constant eigenfunctions. It is proved that L + λI satisfies a strong maximum principle when λ belongs to a suitable pointed left-neighborhood of 0, and satisfies a strong uniform anti-maximum principle when λ 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.