در برخی معادلات غیرمعمول با ضرایب رقابتی

In this paper we study the following nonlocal problems{−(a+b∫R3|∇u|2)Δu+V(x)u=Q(x)up,x∈R3,u∈H1(R3),u>0,x∈R3, where the constants a,b>0, 3<p<5, V(x) and Q(x) are two functions in Clocγ(R3)⋂L∞(R3). By comparing the decay rate of V(x) and Q(x), we first obtain two theorems stating the existence of positive ground states. Under certain assumptions on Q(x), we further prove the existence of positive bound states by using a linking argument with a barycenter map restricted on a Nehari manifold.