| Full text | |
| Author(s): |
Andrade, Joao Henrique
;
Do O, Joao Marcos
Total Authors: 2
|
| Document type: | Journal article |
| Source: | Nonlinearity; v. 35, n. 10, p. 48-pg., 2022-09-01. |
| 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). (AU) | |
| FAPESP's process: | 20/07566-3 - Qualitative properties for higher order and non-local PDEs arising in Differential Geometry |
| Grantee: | João Henrique Santos de Andrade |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |