Existence result for a class of N-Laplacian equations involving critical growth

In this paper, we consider a class of N-Laplacian equations involving critical growth {-ΔNu=λ|u|N-2u+f(x,u),x∈Ω,u∈W01,N(Ω),u(x)≥0,x∈Ω,where Ω is a bounded domain with smooth boundary in ℝN(N >2), f (x, u) is of critical growth. Based on the Trudinger-Moser inequality and a nonstandard linking theorem introduced by Degiovanni and Lancelotti, we prove the existence of a nontrivial solution for any λ > λ1, λ≠λℓ (ℓ = 2,3,ċċċ), and λℓ is the eigenvalues of the operator (-ΔN,W01,N(Ω)), which is defined by the ℤ2-cohomological index.