Open Access Research Article

Optimal Conditions for Maximum and Antimaximum Principles of the Periodic Solution Problem

Meirong Zhang

Author Affiliations

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 2010

Abstract

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.