Profile of Blow-up Solutions to Mean Field Equations with Singular Data

Asymptotic behavior of SU(3) Toda system in a bounded domain

“…See also Lin-Zhang [16] for the Liouville system which is cooperative. Unfortunately, the SU(3) Toda system is not cooperative because of the negative sign in the "off-diagonal" terms in (1). It is unclear if one can still use the method of moving planes.…”

“…See also related studies by OhtsukaSuzuki [20]. In this paper and the subsequent paper [17], we consider the blow-up analysis of solutions to (1). A first natural (and inevitable) question is whether or not there is a boundary bubble.…”

“…Here, ρ 1k and ρ 2k are two positive constants, h 1k (x) and h 2k (x) are two positive functions converging to h 1 (x) and h 2 (x) respectively in C 2,β (Ω) as k → ∞. We are concerned with the asymptotic behavior of unbounded sequences of solutions to (1).…”

“…Furthermore, Chen-Lin [6,7] obtained the sharp estimates for the bubbling rate of solutions to (2) as well as the LeraySchauder degree of all solutions to (2) for all ρ = 8mπ. A related question connected to physics consists in adding Dirac masses to the nonlinear parts, and we refer to Bartolucci-Chen-Lin-Tarantello [1] and to Tarantello [23] for backgrounds, results and asymptotics in this context. Going back to the Toda system (1), Jost-Wang [11] first classified the entire solutions.…”

Singular Limits for 2-Dimensional Elliptic Problem with Exponentially Dominated Nonlinearity and a Quadratic Convection Term

“…This type of equation has been studied by Bartolucci et al in [8] and by Chen and Lin in [10]. They obtained the existence, sharp estimates and construction of multiple bubbles to (4).…”