摘要

In this note, we prove a stability theorem for a class of quasilinear elliptic equations -Delta(p)u = a(x)u - f(x, u) in Omega, u = 0 on partial derivative Omega, where Delta(p)u = div(vertical bar del u vertical bar(p-2)del u), 2 <= p < infinity, Omega subset of R-N is an open, smooth and bounded subset. We show that if u is an unstable solution of the above problem, then u vanishes at some point of Omega. In this work, a and f may change sign.

  • 出版日期2013-10