Research Article
Optimal Conditions for Maximum and Antimaximum Principles of the Periodic Solution Problem
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing 100084, China
Boundary Value Problems 2010, 2010:410986 doi:10.1155/2010/410986
Published: 17 May 2010Abstract
Given a periodic, integrable potential 
, we will study conditions on 
so that the operator 
admits the maximum principle or the antimaximum principle with respect to the periodic
boundary condition. By exploiting Green functions, eigenvalues, rotation numbers,
and their estimates, we will give several optimal conditions.
