Analysis of Blow-up Locus and Existence of Weak Solutions for Nonlinear Supercritical Problems

作者:Wang Kelei; Wei Juncheng*
来源:International Mathematics Research Notices, 2015, (10): 2634-2670.
DOI:10.1093/imrn/rnu013

摘要

We give a qualitative analysis of sequences of stationary solutions to the supercritical problem - Delta u = vertical bar u vertical bar(p-1)u in Omega, p > n+2/n-2. A consequence of the analysis is the existence of positive singular weak solutions on a convex domain when p is an element of(n+2/n-2, n+1/n-3), with only isolated singularities.