A multiple critical points theorem and applications to quasilinear boundary value problems in R+N

In this paper, we prove a multiple critical points theorem and a nonexistence result for the eigenvalues of the pp-Laplacian operator in the half space. As an application, we study the existence of positive (negative) solutions and sign-changing solutions for the boundary value problem of pp-Laplacian equation in the half space, namely: {−Δpu=0in R+N|Du|p−2∂u∂n+λg(x)|u|p−2u=f(u)on ∂R+N, where 1