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:10.1155/2010/410986Published: 17 May 2010
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.