A note on the stability of solutions to quasilinear elliptic equations

Abstract

In this note, we prove a stability theorem for a class of quasilinear elliptic equations -δp u = a(x)u-f(x,u) in Ω, u=0 on δΩ, where δp u= div(/∇uu/ p-2∇u) 2 ≤ p < p < ∞ ,Ω ⊂ &RdblN 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 Ω. In this work, a and f may change sign.