Qualitative properties for solutions to subcritical fourth order systems. (English) Zbl 1498.35238
Summary: 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 J. Serrin [Acta Math. 111, 247–302 (1964; Zbl 0128.09101)], P.-L. Lions [J. Differ. Equations 38, 441–450 (1980; Zbl 0458.35033)], P. Aviles [Commun. Math. Phys. 108, No. 2, 177–192 (1987; Zbl 0617.35040)], and B. Gidas and J. Spruck [Commun. Pure Appl. Math. 34, 525–598 (1981; Zbl 0465.35003)]. 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 R. Soranzo [Potential Anal. 6, No. 1, 57–85 (1997; Zbl 0877.35006)].
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