Abstract
This paper is devoted to a class of important and general nonlocal fourth order elliptic problemΔ2u−(1+λ∫R3|∇u|2dx)Δu+V(x)u=f(x,u) in R3, where Δ2=Δ(Δ) is the bi-harmonic operator, λ≥0 is a constant. We focus on the case that f(x,u) involves a combination of convex and concave terms and the potential V(x) is allowed to be sign-changing. By new techniques, multiplicity results of two different type of solutions are established. Our results improves and generalizes that obtained in the literature.
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