Nonlinear elliptic problems with a singular weight on the boundary

作者：Davila Juan; Peral Ireneo^*

来源：Calculus of Variations and Partial Differential Equations, 2011, 41(3-4): 567-586.

DOI：10.1007/s00526-010-0376-5

We study existence of solutions to
-Delta u = u(p)/|x|(2) u > 0 in Omega
with u = 0 on partial derivative Omega, where Omega is a smooth bounded domain in R(N), N >= 3 with 0 is an element of partial derivative Omega and 1 < p < N+2/N-2. The existence of solutions depends on the geometry of the domain. On one hand, if the domain is starshaped with respect to the origin there are no energy solutions. On the other hand, in dumbbell domains via a perturbation argument, the equation has solutions.

• 出版日期2011-7