Existence of nontrivial solutions for a biharmonic equation with p-Laplacian and singular sign-changing potential

Abstract

In the paper, we study a class of biharmonic equations with p -Laplacian and singular sign-changing potential as follows: Δ 2 u − β Δ p u + V λ ( x ) u = 0 in R N , u ∈ H 2 ( R N ) , where N ≥ 5 , β < 0 , Δ p u = div ( | ∇ u | p − 2 ∇ u ) with p ≥ 2 and V λ ( x ) = λ a ( x ) − b ( x ) with λ > 0 . Under some suitable assumptions on a and b , we obtain the existence of nontrivial solutions for λ large enough.