We study positive solutions to the following higher order SchrSdinger system with Dirichlet boundary conditions on a half space： where a is any even number between 0 and n. This PDE system is closely related to the i...We study positive solutions to the following higher order SchrSdinger system with Dirichlet boundary conditions on a half space： where a 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.展开更多
基金supported by China Scholarship Council(Grant No.201206060010)
文摘We study positive solutions to the following higher order SchrSdinger system with Dirichlet boundary conditions on a half space： where a 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.
