Convergence for a Liouville equation

Ma, Li; Wei, Juncheng

doi:10.1007/pl00013216

Cited by 96 publications

(82 citation statements)

References 21 publications

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“…In this paper we prove that such a family indeed exists if Ω is not simply connected. In case of existence, location of blowing-up points is well-understood: it is established in [27,30] The proofs in [27,30] are actually for the case k ≡ 1 but, as pointed out in [25], they apply to the general case. Obvious question is the reciprocal, namely presence of multiple-bubbling solutions with concentration at a critical point of ϕ m .…”

Section: Introduction and Statement Of Main Resultsmentioning

confidence: 99%

Singular limits in Liouville-type equations

2005

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Abstract. We consider the boundary value problem ∆u + ε 2 k(x) e u = 0 in a bounded, smooth domain Ω in R 2 with homogeneous Dirichlet boundary conditions. Here ε > 0, k(x) is a non-negative, not identically zero function. We find conditions under which there exists a solution uε which blows up at exactly m points as ε → 0 and satisfies ε 2 Ω ke u ε → 8mπ. In particular, we find that if k ∈ C 2 (Ω), infΩ k > 0 and Ω is not simply connected then such a solution exists for any given m ≥ 1

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Section: Introduction and Statement Of Main Resultsmentioning

confidence: 99%

Singular limits in Liouville-type equations

2005

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“…We summarize some known results. Let (u k , ρ k ) be a blow-up sequence of solutions to (2) with ρ k uniformly bounded, then it was proved that (P1) (no boundary bubbles) u k is uniformly bounded near a neighborhood of ∂Ω (Nagasaki-Suzuki [19], Ma-Wei [18]);…”

Section: Introductionmentioning

confidence: 99%

“…Such a question will not arise in system (6). In the case of single equation (2), boundary blow-up is excluded by the method of moving planes and the use of Kelvin's transform ( [18]). This technique works well for elliptic systems too, provided that the system is cooperative.…”

Section: Introductionmentioning

confidence: 99%

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

2011

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“…See [Cheng and Ni 1991] and [Lin 2007] for deep results on the mean field equations and related topics. See also [Ma and Wei 2001] and [Tarantello 2004]. …”

Section: Mamentioning

confidence: 99%