A nonlinear boundary problem involving the p-bilaplacian operator

Abstract

We show some new Sobolev's trace embedding that we apply to prove that the fourth-order nonlinear boundary conditions Δp2u+|u|p−2u=0 in Ω and −(∂/∂n)(|Δu|p−2Δu)=λρ|u|p−2u on ∂Ω possess at least one nondecreasing sequence of positive eigenvalues.