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A variational analysis of the Toda system on compact surfaces
 Comm. Pure Appl. Math
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Malchiodi A.: An improved Geometric Inequality via Vanishing Moments, with Applications to Singular Liouville Equations
 Commun. Math. Phys
, 2013
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ON THE SOLVABILITY OF SINGULAR LIOUVILLE EQUATIONS ON COMPACT SURFACES OF ARBITRARY GENUS
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LOCAL PROFILE OF FULLY BUBBLING SOLUTIONS TO SU(N+1) TODA SYSTEMS
"... ABSTRACT. In this article we prove that for locally defined singular SU(n + 1) Toda systems in R 2, the profile of fully bubbling solutions near the singular source can be accurately approximated by global solutions. The main ingredients of our new approach are the classification theorem of LinWei ..."
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ABSTRACT. In this article we prove that for locally defined singular SU(n + 1) Toda systems in R 2, the profile of fully bubbling solutions near the singular source can be accurately approximated by global solutions. The main ingredients of our new approach are the classification theorem of LinWeiYe [20] and the nondegeneracy of the linearized Toda system [20], which make us overcome the difficulties that come from the lack of symmetry and the singular source. 1.
A continuum of solutions for the SU(3) Toda system exhibiting partial blowup, preprint arXiv:1407.8407
"... ABSTRACT. In this paper we consider the socalled Toda System in planar domains under Dirichlet boundary condition. We show the existence of continua of solutions for which one component is blowing up at a certain number of points. The proofs use singular perturbation methods. ..."
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ABSTRACT. In this paper we consider the socalled Toda System in planar domains under Dirichlet boundary condition. We show the existence of continua of solutions for which one component is blowing up at a certain number of points. The proofs use singular perturbation methods.
On Nontopological Solutions of the A2 and
, 2013
"... For any rank 2 of simple Lie algebra, the relativistic ChernSimons system has the following form: ∆u1 + ( ∑2 i=1K1ie ui −∑2i=1∑2j=1 euiK1ieujKij) = 4pi N1∑ j=1 δpj ∆u2 + ( ∑2 i=1K2ie ui −∑2i=1∑2j=1 euiK2ieujKij) = 4pi N2∑ j=1 δqj in R2, (0.1) where K is the Cartan matrix of rank 2. There are thre ..."
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For any rank 2 of simple Lie algebra, the relativistic ChernSimons system has the following form: ∆u1 + ( ∑2 i=1K1ie ui −∑2i=1∑2j=1 euiK1ieujKij) = 4pi N1∑ j=1 δpj ∆u2 + ( ∑2 i=1K2ie ui −∑2i=1∑2j=1 euiK2ieujKij) = 4pi N2∑ j=1 δqj in R2, (0.1) where K is the Cartan matrix of rank 2. There are three Cartan matrix of rank 2: A2, B2 and G2. A longstanding open problem for (0.1) is the question of the existence of nontopological solutions. In this paper, we consider the A2 and B2 case. We prove the existence of nontopological solutions under the condition that either ∑N1 j=1 pj =∑N2 j=1 qj or ∑N1 j=1 pj 6=
j=1
, 2012
"... For any rank 2 of simple Lie algebra, the relativistic ChernSimons system has the following form: ..."
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For any rank 2 of simple Lie algebra, the relativistic ChernSimons system has the following form: