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Indexed by:期刊论文

Date of Publication:2015-01-01

Journal:SCIENCE CHINA-MATHEMATICS

Included Journals:SCIE、Scopus

Volume:58

Issue:1

Page Number:179-196

ISSN No.: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.