Sign-changing solutions for fractional Schrödinger–Poisson system in ℝ3

We consider the existence of sign-changing solutions for the following fractional Schrödinger–Poisson system (-Δ)su+V(x)u+λϕ(x)u=f(u),&x∈R3,(-Δ)tϕ=u2,&x∈R3, where s,t∈(0,1), λ is a positive parameter, V(x):R3→R+ is a continuous potential function. Since multiple nonlocal terms are involving in the system, some new techniques are applied to prove the existence of a least energy sign-changing solution uλ. Moreover, we prove that the energy of any sign-changing solution to this system is strictly larger than twice of the ground state energy. Furthermore, the asymptotic behavior of uλ as λ→0+ is also analyzed.