Analytic aspects of the Toda system: II. Bubbling behavior and existence of solutions

Elliptic functions, Green functions and the mean field equations on tori

“…Recently it was shown to be related to the self dual condensation of the Chern-Simons-Higgs model. We refer to [3], [4], [2], [5], [6], [8], [9] and [10] for the recent development of this subject. When ¤ 8m for any m 2 ‫,ޚ‬ it has been recently proved in [4], [2], [5] that the Leray-Schauder degree is nonzero; so the equation always has solutions, regardless of the actual shape of T .…”

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

“…Thus Proposition 2.4 of [10] shows that (σ 1i , σ 2i ) of Lemma 3.10 can only be one of (4π, 0), (0, 4π), (4π, 8π), (8π, 4π) or (8π, 8π). Finally, sinceũ 1k → −∞ and u 2k → −∞ locally in Ω \ S, …”

“…Jost-Wang [12] and Jost-Lin-Wang [10] studied the SU(3) Toda system on a two-dimensional manifold M without boundary…”

Sharp asymptotics and compactness for local low energy solutions of critical elliptic systems in potential form

“…They have been the target of investigations for decades and are currently subject to an intensive research activity. Without any pretention to exhaustivity, we mention that possible references on elliptic systems are Amster et al [1], Angenent and Van der Vorst [2,3], Clément et al [13], De Figueiredo [14], De Figueiredo and Ding [15], De Figueiredo and Felmer [16], De Figueiredo and Sirakov [17], El Hamidi [21], Giaquinta and Martinazzi [22], Hebey [28][29][30], Hulshof et al [33], Jost et al [34], Jost and Wang [35], Mancini and Mitidieri [42], Mitidieri and Sweers [44], Montenegro [45], Pompino [47], Qing [48], and Sweers [60].…”