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

Abstract EN

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 ∇ u N - 2 ∇ u + V x u N - 2 u = λ u N - 2 u / x β + f x , u / x β + ɛ h x , x ∈ ℝ N , u ≠ 0 , x ∈ ℝ N , where 0 < β < N , V ( x ) is an indefinite weight, f : ℝ N × ℝ → ℝ behaves like exp α u N / N - 1 and does not satisfy the Ambrosetti-Rabinowitz condition, and h ∈ ( W 1 , N ( ℝ N ) ) * .