We show some new Sobolev's trace embedding that we apply to prove that the fourth-order nonlinear boundary conditions Δ p 2 u + | u | p − 2 u = 0 in Ω and − ( ∂ / ∂ n ) ( | Δ u | p − 2 Δ u ) = λ ρ | u | p − 2 u on ∂ Ω possess at least one nondecreasing sequence of positive eigenvalues.