Positive solution for an indefinite fourth-order nonlocal problem

We prove the existence of a positive solution for the problem γΔ 2 u − m ( u ) Δ u = μ a ( x ) u q + b ( x ) u p , in Ω, u = γΔ u = 0 , on ∂ Ω, where Ω ⊂ ℝ N is a bounded smooth domain, γ ∈ {0, 1},0 < q > 1 < p, m is weakly continuous in H 2 ( Ω ) ∩ H 0 1 ( Ω ) , a ∈ L ∞ ( Ω ) is nonnegative and b is a bounded potential which can change sign. The solution is obtained via a sub-supersolution approach when the parameter µ > 0 is small.