WIAS Preprint No. 2026, (2014)
Bifurcation results for a fractional elliptic equation with critical exponent in $R^n$
- Dipierro, Serena
- Medina, Maria
- Peral, Ireneo
- Valdinoci, Enrico
2010 Mathematics Subject Classification
- 5B40 35D30 35J20 35R11 49N60
- Bifurcation, Lyapunov-Schmidt reduction, critical problem, fractional elliptic regularity
In this paper we study some nonlinear elliptic equations obtained as a perturbation of the problem with the fractional critical Sobolev exponent. To construct solutions to this equation, we use the Lyapunov-Schmidt reduction, that takes advantage of the variational structure of the problem. Some cases of the parameter range are particularly difficult, due to the lack of regularity of the associated energy functional, and we need to introduce a new functional setting and develop an appropriate fractional elliptic regularity theory.
- Manuscripta Math., 153 (2017) pp. 183-230.