Qualitative properties for solutions to subcritical fourth order systems* *This work was partially supported by Fulbright Commission in Brazil #G-1-00001, Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) #312340/2021-4 and #429285/2016-7, Fundação de Apoio à Pesquisa do Estado da Paraíba (FAPESQ) #3034/2021, Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) #88882.440505/2019-01, and Fundação de Amparo à Pesquisa do Estado

Abstract

We prove some qualitative properties for singular solutions to a class of strongly coupled system involving a Gross–Pitaevskii-type nonlinearity. Our main theorems are vectorial fourth order counterparts of the classical results due to Serrin (1964 Acta Math. 111 247–252), Lions (1980 J. Differ. Equ. 38 441–450), Aviles (1987 Commun. Math. Phys. 108 177–192), and Gidas and Spruck (1981 Commun. Pure Appl. Math. 34 525–598). On the technical level, we use the moving sphere method to classify the limit blow-up solutions to our system. Besides, applying asymptotic analysis, we show that these solutions are indeed the local models near the isolated singularity. We also introduce a new fourth order nonautonomous Pohozaev functional, whose monotonicity properties yield improvement for the asymptotics results due to Soranzo (1997 Potential Anal. 6 57–85).