In this paper, we consider the following new nonlocal problem:-(a-b Ω |∇u| 2 dx) u = λf (x)|u| p-2 u, x ∈ Ω, u = 0, x ∈ ∂Ω, where Ω is a smooth bounded domain in R 3 , a, b > 0 are constants, 3 < p < 6, and the parameter λ > 0. Under some assumptions on the sign-changing function f , we obtain the existence of positive solutions via variational methods.
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