(untitled) (Journal of Partial Differential Equations, 2013)
Using variational methods, we prove the existence of a nontrivial weak solution for the problem align* { arrayll -_i=1^N_x_i(|_x_iu|^p_i-2_x_iu) =λ a(x)|u|^q(x)-2u+|u|^p^*-2u, & in Ω, u = 0, & in Ω, array . align* where Ω R^N (N ≥ 3) is a bounded domain with smooth boundary Ω, 2 ≤ p_i < N, i = 1, N, q: Ω → (1, p^*) is a continuous function, p^*=N_i=1^N 1p_i-1 is the critical exponent for this class of problem, and λ is a parameter.