A Variational Analysis of the Toda System on Compact Surfaces

作者：Malchiodi Andrea^*; Ruiz David

来源：Communications on Pure and Applied Mathematics, 2013, 66(3): 332-371.

DOI：10.1002/cpa.21433

In this paper we consider the following Toda system of equations on a compact surface: %26lt;br%26gt;{Delta u(1) = 2 rho(1)(h(1)e(u1)/integral(Sigma)h(1)e(u1) dV(g) - 1) - rho(2)(h(2)e(u2)/integral(Sigma)h(2)e(u2) dV(g) - 1), %26lt;br%26gt;{Delta u(2) = 2 rho(2)(h(2)e(u2)/integral(Sigma)h(2)e(u2) dV(g) - 1) - rho(1)(h(1)e(u1)/integral(Sigma)h(1)e(u1) dV(g) - 1). %26lt;br%26gt;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 u(1) and u(2).

• 出版日期2013-3