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{-?N u = λ|u|N-2 u + f（x, u）, x ∈ ?,u ∈ W01,N（?）, u（x） ≥ 0, x ∈ ?,where ? 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 = λ?（? = 2, 3, ···）, and λ? is the eigenvalues of the operator(-?N, W01,N（?）),which is defined by the Z2-cohomological index.