Nontrivial solutions for Schr?dinger-Kirchhoff-type problem in RN

摘要

In the present paper, we use variational methods to prove two existence results of nontrivial solutions for the Schr?dinger-Kirchhoff-type problem { ? ( a + b ∫ R N | ? u | 2 d x ) △ u + V ( x ) u = f ( x , u ) , for x ∈ R N , u ( x ) → 0 , as | x | → ∞ .