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A classification of solutions of a conformally invariant fourth order equation in Rn
Abstract. In this paper, we consider the following conformally invariant equations of fourth order¶ $ \cases {\Delta^2 u = 6 e^{4u} &in $\bf {R}^4,$ \cr e^{4u} \in L^1(\bf {R}^4),\cr}$(1)¶and¶ $Expand
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Large amplitude stationary solutions to a chemotaxis system
Pour des fonctions positives u et v, on considere le systeme D 1 Δu-χ⊇•(u⊇logv)=0, D 2 Δv-av+bu=0 dans Ω; ∂u/∂n=∂v/οn=0 sur ∂Ω, |Ω| −1 ∫ Ω u(x)dx=ū, ou |Ω| est le volume de Ω et ū>0 est une constanteExpand
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Topological degree for a mean field equation on Riemann surfaces
We consider the following mean field equations: (0.1) where M is a compact Riemann surface with volume 1, h is a positive continuous function on M, ρ is a real number, (0.2) Expand
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Sharp estimates for solutions of multi-bubbles in compact Riemann surfaces
In this paper, we consider a sequence of multibubble solutions u k of the equation (0.1) Δ 0 u k + ρ k (he uk /f M he u k d μ -1)=0 in M, where h is a C 2,β positive function in a compact RiemannExpand
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Estimates of the conformal scalar curvature equation via the method of moving planes
In this paper we derive a local estimate of a positive singular solution u near its singular set Z of the conformal equation where K(x) is a positive continuous function, Z is aExpand
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Interpolation inequalities with weights
We use elementary methods to prove a sufficient and necessary condition for a Sobolev interpolation inequalities with weight [ILLM0001] where [ILLM0001] are real numbers, and [ILLM0001]
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Classification and nondegeneracy of SU(n+1) Toda system with singular sources
AbstractWe consider the following Toda system where γi>−1, δ0 is Dirac measure at 0, and the coefficients aij form the standard tri-diagonal Cartan matrix. In this paper, (i) we completely classifyExpand
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Existence of positive weak solutions with a prescribed singular set of semilinear elliptic equations
AbstractIn this paper, we consider the problem of the existence of non-negative weak solution u of % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn%Expand
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