ON THE LOCATION OF A PEAK POINT OF A LEAST ENERGY SOLUTION FOR HENON EQUATION

Abstract

Let Omega be a smooth bounded domain. We are concerned about the following nonlinear elliptic problem: {Delta u + vertical bar x vertical bar(alpha)u(p) = 0, u > 0 in Omega, u = 0 on partial derivative Omega, where alpha > 0, p is an element of (1, n+2/n 2). In this paper, we show that for n >= 8, a maximum point x(alpha) of a least energy solution of above problem converges to a point x(0) is an element of partial derivative*Omega satisfying H(x(0)) = min(omega is an element of partial derivative*Omega) H(omega) as alpha -> infinity, where H is the mean curvature on partial derivative Omega and partial derivative*Omega {x is an element of partial derivative Omega : vertical bar x vertical bar >= vertical bar y vertical bar for any y is an element of Omega}.