| Full text | |
| Author(s): |
Andrade, Joao Henrique
;
Wei, Juncheng
Total Authors: 2
|
| Document type: | Journal article |
| Source: | NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS; v. 255, p. 28-pg., 2025-06-01. |
| Abstract | |
We classify the local asymptotic behavior of positive singular solutions to a class of subcritical sixth order equations on the punctured ball. First, using a version of the integral moving spheres technique, we prove that solutions are asymptotically radially symmetric solutions with respect to the origin. We divide our approach into some cases concerning the growth of nonlinearity. In general, we use an Emden-Fowler change of variables to translate our problem to a cylinder. In the lower critical regime, this is not enough, thus, we need to introduce a new notion of change of variables. The main difficulty is that the cylindrical PDE in this coordinate system is nonautonomous. Nonetheless, we define an associated nonautonomous Pohozaev functional, which can be proved to be asymptotically monotone. In addition, we show a priori estimates for these two functionals, from which we extract compactness properties. With these ingredients, we can perform an asymptotic analysis technique to prove our main result. (AU) | |
| FAPESP's process: | 23/15567-8 - Qualitative properties for geometric differential equations |
| Grantee: | João Henrique Santos de Andrade |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 21/15139-0 - Qualitative properties for fourth order PDEs arising in differential geometry |
| Grantee: | João Henrique Santos de Andrade |
| Support Opportunities: | Scholarships abroad - Research Internship - Post-doctor |
| 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 |