On the Existence of Solutions for a Class of Schrödinger–Kirchhoff-Type Equations with Sign-Changing Potential - Guocui Yang; Jianwen Zhou; Shengzhong Duan (Discrete Dynamics in Nature and Society)
In this paper, we consider the following Kirchhoff problem −a+b∫R3∇u2dxΔu+λVxu=up−2u, in R3u∈H1R3 where a,b>0 are constants, λ is a positive parameter, and 4<p<6. Under suitable assumptions on Vx, the existence of nontrivial solution is obtained via variational methods. The potential Vx is allowed to be sign-changing.