Multiple Solutions for a Class of N-Laplacian Equations with Critical Growth and Indefinite Weight

Abstract

Using the suitable Trudinger-Moser inequality and the Mountain Pass Theorem, we prove the existence of multiple solutions for a class of N-Laplacian equations with critical growth and indefinite weight -div∇uN-2∇u+VxuN-2u=λuN-2u/xβ+fx,u/xβ+ɛhx, x∈ℝN, u≠0, x∈ℝN, where 0<β<N, V(x) is an indefinite weight, f:ℝN×ℝ→ℝ behaves like exp⁡αuN/N-1 and does not satisfy the Ambrosetti-Rabinowitz condition, and h∈(W1,N(ℝN))*.