Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2015-01-01

Journal: SCIENCE CHINA-MATHEMATICS

Included Journals: Scopus、SCIE

Volume: 58

Issue: 1

Page Number: 179-196

ISSN: 1674-7283

Key Words: Schrodinger systems; poly-harmonic operators; Dirichlet boundary conditions; method of moving planes in integral forms; Kelvin transforms; monotonicity; rotational symmetry; non-existence

Abstract: We study positive solutions to the following higher order Schrodinger system with Dirichlet boundary conditions on a half space: where alpha is any even number between 0 and n. This PDE system is closely related to the integral system where G is the corresponding Green's function on the half space. More precisely, we show that every solution to (0.2) satisfies (0.1), and we believe that the converse is also true. We establish a Liouville type theorem - the non-existence of positive solutions to (0.2) under a very weak condition that u and v are only locally integrable. Some new ideas are involved in the proof, which can be applied to a system of more equations.