Maximum principles for linear difference-differential operators in periodic function spaces

1984 ◽  
Vol 43 (1) ◽  
pp. 121-139 ◽  
Author(s):  
Marino Zennaro
Keyword(s):  
Periodic Function ◽  
Differential Operators ◽  
Function Spaces ◽  
Maximum Principles

scholarly journals MAXIMUM PRINCIPLES AROUND AN EIGENVALUE WITH CONSTANT EIGENFUNCTIONS

2008 ◽  
Vol 10 (06) ◽  
pp. 1243-1259 ◽  
Author(s):  
J. CAMPOS ◽  
J. MAWHIN ◽  
R. ORTEGA
Keyword(s):  
Maximum Principle ◽  
Boundary Conditions ◽  
Differential Operators ◽  
Neumann Boundary ◽  
Function Spaces ◽  
Strong Maximum Principle ◽  
Neumann Boundary Conditions ◽  
Linear Operators ◽  
Maximum Principles ◽  
Partial Differential Operators

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.

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