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 { - Δ N u = λ | u | N - 2 u + f ( x , u ) , x ∈ Ω , u ∈ W 0 1 , N ( Ω ) , u ( x ) ≥ 0 , x ∈ Ω , where Ω is a bounded domain with smooth boundary in ℝ N ( 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 > λ 1 , λ≠λ l (l = 2,3,ċċċ), and λ l is the eigenvalues of the operator ( - Δ N , W 0 1 , N ( Ω ) ) , which is defined by the ℤ 2 -cohomological index.