Singular limits for the bi-Laplacian operator with exponential nonlinearity in R-4

Abstract

Let Omega be a bounded smooth domain in R-4 such that for some integer d >= 1 its d-th singular cohomology group with coefficients in some field is not zero, then problem {Delta(2)u - rho(4)k(x)e(u) = 0 in Omega,

u = Delta u = 0 on partial derivative Omega,

has a solution blowing-up, as rho -> 0, at m points of Omega, for any given number in.