ISOLATED SINGULARITIES OF POSITIVE SOLUTIONS OF A SUPERLINEAR BIHARMONIC EQUATION

This paper is mainly concerned with the local behavior of singular sol utions of the biharmonic equation Delta(2)u = \x\(sigma)u(p) with u gr eater than or equal to 0 in Omega\{0} subset of R(N),N greater than or equal to 4, and Omega = B(0,R) is a ball centered at the origin of ra dius R > 0. The complete description of the singularity together with an existence result will be given when 1 < p < N+sigma/N-4, -4 < sigma less than or equal to 0, for N >, or 1 < p < +infinity, for N = 4. Mo reover, an a priori estimate of the radially symmetric solutions will be established when p greater than or equal to N+sigma/N-4, -4 < sigma less than or equal to 0,N > 4. This paper generalizes the results in Brezis and Lions (1981) and Lions (1980) for the corresonding Laplace equation.