Nontrivial solution for Klein-Gordon equation coupled with Born-Infeld theory with critical growth

Chuan-Min He, Lin Li, Shang-Jie Chen

In this paper, we study the following system \begin{eqnarray*} \left\{ \begin{array}{ll} -Δu + V(x)u-(2ω+ϕ)ϕu=λf(u)+|u|^{4}u, \ & \text{in} \ \mathbb{R}^{3}, Δϕ+ βΔ_4ϕ= 4π(ω+ϕ) u^{…