Solutions for a Fractional Kirchhoff–Choquard Equation

In this paper, we mainly study the fractional elliptic equation: (a+b∫_R³|(-Δ)s/2u|²dx)(-Δ)ˢu+u=(|x|-μ*|u|ᵖ)|u|ᵖ⁻²u, x³, where μ∈(0,3) , s∈(0,1) , 2-μ/3<p<6-μ/3-2s , $$a,b>0$$ . For this equation, we will discuss it in two case. For s∈(0,3/4] , we prove the existence of solutions by establishing an equivalent system. For s∈(3/4,1) , we use the symmetric mountain pass lemma to prove that the equation has infinitely many solutions.