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22
Analytic aspects of the Toda system: II. Bubbling behavior and existence of solutions
, 2005
"... In this paper, we continue to consider the 2dimensional (open) Toda system (Toda lattice) for SU(N + 1) N∑ ..."
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Cited by 39 (17 self)
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In this paper, we continue to consider the 2dimensional (open) Toda system (Toda lattice) for SU(N + 1) N∑
ELLIPTIC FUNCTIONS, GREEN FUNCTIONS AND THE MEAN FIELD EQUATIONS ON TORI
, 2006
"... ABSTRACT. We show that the Green functions on flat tori can have either 3 or 5 critical points only. There does not seem to be any direct method to attack this problem. Instead, we have to employ sophisticated nonlinear partial differential equations to study it. We also study the distribution of n ..."
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Cited by 28 (5 self)
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ABSTRACT. We show that the Green functions on flat tori can have either 3 or 5 critical points only. There does not seem to be any direct method to attack this problem. Instead, we have to employ sophisticated nonlinear partial differential equations to study it. We also study the distribution of number of critical points over the moduli space of flat tori through deformations. The functional equations of special theta values provide important inequalities which lead to a solution for all rhombus tori. The general picture is also emerged, though some of the necessary technicality is still to de developed. 1.
Topological methods for an elliptic equations with exponential nonlinearities
"... abstract. We consider a class of variational equations with exponential nonlinearities on compact surfaces. From considerations involving the MoserTrudinger inequality, we characterize some sublevels of the EulerLagrange functional in terms of the topology of the surface and of the data of the equ ..."
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Cited by 17 (6 self)
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abstract. We consider a class of variational equations with exponential nonlinearities on compact surfaces. From considerations involving the MoserTrudinger inequality, we characterize some sublevels of the EulerLagrange functional in terms of the topology of the surface and of the data of the equation. This is used together with a minmax argument to obtain existence results.
Solutions for Toda systems on Riemann surfaces
 Ann. Scuola Norm. Sup. Pisa Cl. Sci
"... Abstract. In this paper, we study the solutions of Toda systems on Riemann surface in the critical case, we prove a sufficient condition for the existence of solutions of Toda systems. Dedicated to Professor Ding Weiyue on the occasion of his 60’s birthday. 1. ..."
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Cited by 10 (2 self)
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Abstract. In this paper, we study the solutions of Toda systems on Riemann surface in the critical case, we prove a sufficient condition for the existence of solutions of Toda systems. Dedicated to Professor Ding Weiyue on the occasion of his 60’s birthday. 1.
The logarithmic HLS inequality for systems on compact manifolds
"... We prove an optimal logarithmic HardyLittlewoodSobolev inequality for systems on compact mdimensional Riemannian manifolds, for any m ≥ 2. We show that a special case of the inequality, involving only two functions, implies the general case by using an argument from the theory of Linear Programin ..."
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Cited by 4 (2 self)
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We prove an optimal logarithmic HardyLittlewoodSobolev inequality for systems on compact mdimensional Riemannian manifolds, for any m ≥ 2. We show that a special case of the inequality, involving only two functions, implies the general case by using an argument from the theory of Linear Programing. 2
A note on compactness properties of the singular Toda system
"... In this note, we consider blowup for solutions of the SU(3) Toda system on a compact surface Σ. In particular, we give a complete proof of the compactness result stated by Jost, Lin and Wang in [11] and we extend it to the case of singularities. This is a necessary tool to find solutions through va ..."
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Cited by 2 (0 self)
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In this note, we consider blowup for solutions of the SU(3) Toda system on a compact surface Σ. In particular, we give a complete proof of the compactness result stated by Jost, Lin and Wang in [11] and we extend it to the case of singularities. This is a necessary tool to find solutions through variational methods.
and
, 2004
"... We study noncompact solution sequence to the $SU(3) $ Toda system in nonabelian relativistic selfdual gauge theory, i.e., the quantization of the total mass and classification of the singular limit. ..."
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We study noncompact solution sequence to the $SU(3) $ Toda system in nonabelian relativistic selfdual gauge theory, i.e., the quantization of the total mass and classification of the singular limit.
Abstract We prove that the solution to the SU(3) Toda system
, 2010
"... u − ev = 0 in R2, ∆v − eu + 2ev = 0 in R2 ∫ e u ∫ < ∞, e v < ∞, R 2 R 2 is nondegenerate, i.e., the kernel of the linearized operator is exactly eightdimensional. 1 ..."
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u − ev = 0 in R2, ∆v − eu + 2ev = 0 in R2 ∫ e u ∫ < ∞, e v < ∞, R 2 R 2 is nondegenerate, i.e., the kernel of the linearized operator is exactly eightdimensional. 1
für Mathematik in den Naturwissenschaften Leipzig
, 2002
"... On a nonlinear elliptic equation arising in a free boundary problem by ..."
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