Critical exponents and critical dimensions for quasilinear elliptic problems

The main purpose of this paper is to discuss the critical dimension phenomenon for sign-changing solutions of the following quasilinear elliptic problem involving critical Sobolev exponent: {−Δpu=|u|p∗−2u+λ|u|q−2u,x∈B1,u|∂B1=0, where B1⊂RNB1⊂RN is a unit ball centered at the origin, Δpu=div(|∇u|p−2∇u),λ>0,2≤pp(pq−q+1)1+(q−p)(p−1).