Qualitative properties for solutions to subcritical fourth order systems*

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