Optimal Conditions for Maximum and Antimaximum Principles of the Periodic Solution Problem. (17th May 2010) - Zhang Zhang, Meirong Meirong
Abstract : Given a periodic, integrable potential q ( t ), we will study conditions on q ( t ) so that the operator L q x = x ″ + q x 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.