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Vector Solutions with Prescribed Component-Wise Nodes for a Schrödinger System

Year:    2019

Analysis in Theory and Applications, Vol. 35 (2019), Iss. 3 : pp. 288–311

Abstract

For the Schrödinger system

{Δuj+λjuj=ki=1βiju2iujin    RN,uj(x)0 as   |x|,j=1,,k,

where k2 and N=2,3, we prove that for any λj>0 and βjj>0 and any positive integers pj, j=1,2,,k, there exists b>0 such that if βij=βjib for all ij then there exists a radial solution (u1,u2,,uk) with uj having exactly pj1 zeros. Moreover, there exists a positive constant C0 such that if βij=βjib (ij) then any solution obtained satisfies

ki,j=1|βij|RNu2iu2jC0.

Therefore, the solutions exhibit a trend of phase separations as βij for ij.

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ata.OA-0009

Analysis in Theory and Applications, Vol. 35 (2019), Iss. 3 : pp. 288–311

Published online:    2019-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    24

Keywords:    Vector solution prescribed component-wise nodes Schrödinger system variational methods.

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