Existence of weak solutions for a quasilinear equation in

This paper studies the p -Laplacian equation − Δ p u + λ V λ ( x ) | u | p − 2 u = f ( x , u ) in R N , where 1 < p < N , λ ≥ 1 and V λ ( x ) is a nonnegative continuous function. Under some conditions on f ( x , u ) and V λ ( x ) , we prove the existence of nontrivial solutions for λ sufficiently large.