A multiple critical points theorem and applications to quasilinear boundary value problems in [formula omitted

Abstract

In this paper, we prove a multiple critical points theorem and a nonexistence result for the eigenvalues of the p-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 p-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<p<N,Δpu=div(|Du|p−2Du),λ is a positive parameter, g is a nonnegative function and f is p-superlinear at zero and asymptotically p-linear at infinity.