A Variational Analysis of the Toda System on Compact Surfaces. Issue 3 (14th November 2012) - Malchiodi, Andrea; Ruiz, David
Abstract In this paper we consider the following Toda system of equations on a compact surface: <alternatives> <![CDATA[articlemathrsfsamsmathemptydocumentalign* cases - Δ u_1 = 2 ρ_1 ( h_1 e^u_1h_1 e^u_1 dV_g - 1 ) - ρ_2 ( h_2 e^u_2h_2 e^u_2 dV_g - 1 ), [2] - Δ u_2 = 2 ρ_2 ( h_2 e^u_2h_2 e^u_2 dV_g - 1 ) - ρ_1 ( h_1 e^u_1h_1 e^u_1 dV_g - 1 ) cases. align* document]]> </alternatives> We will give existence results by using variational methods in a noncoercive case. A key tool in our analysis is a new Moser‐Trudinger type inequality under suitable conditions on the center of mass and the scale of concentration of the two components u1 and u2. © 2012 Wiley Periodicals, Inc.