Infinitely many solutions for a class of fractional Schrodinger equations coupled with neutral scalar field

We study the fractional Schr\"{o}dinger equations coupled with a neutral scalar field (-Δ)ˢ u+V(x)u=K(x)φ u +g(x)|u|q-2u, x∈ R³, (I-Δ)ᵗ φ=K(x)u², x∈ R³, where (-Δ)ˢ and (I-Δ)ᵗ denote the fractional Laplacian and Bessel operators with 3/4 <s<1 and $0<t<1$, respectively. Under some suitable assumptions for the external potentials V, K and g, given q∈(1,2)∪(2,2ₛ^*) with 2ₛ^*:= 6/3-2s, with the help of an improved Fountain theorem dealing with a class of strongly indefinite variational problems approached by Gu-Zhou [Adv. Nonlinear Stud., { 17} (2017), 727--738], we show that the system admits infinitely many nontrivial solutions.