The aim of this note is to present the first qualitative global bifurcation diagram of the equation $-\Delta u=\mu|x|^{2\alpha}e^u$. To this end, we introduce the notion of domains of first/second kind for singular mean field equations and base our approach on a suitable spectral analysis. In particular, we treat also non-radial solutions and non-symmetric domains and show that the shape of the branch of solutions still resembles the well-known one of the model regular radial case on the disk. Some work is devoted also to the asymptotic profile for $\mu\to-\infty$.
Bartolucci, D., Jevnikar, A., R., W. (2024). On the global bifurcation diagram of the equation −∆u = µ|x| 2α e u in dimension two. DIFFERENTIAL AND INTEGRAL EQUATIONS, 37(7-8), 425-442.
On the global bifurcation diagram of the equation −∆u = µ|x| 2α e u in dimension two
Bartolucci, D;Jevnikar, A;
2024-01-01
Abstract
The aim of this note is to present the first qualitative global bifurcation diagram of the equation $-\Delta u=\mu|x|^{2\alpha}e^u$. To this end, we introduce the notion of domains of first/second kind for singular mean field equations and base our approach on a suitable spectral analysis. In particular, we treat also non-radial solutions and non-symmetric domains and show that the shape of the branch of solutions still resembles the well-known one of the model regular radial case on the disk. Some work is devoted also to the asymptotic profile for $\mu\to-\infty$.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
