Existence of positive solutions for nonlocal problems with indefinite nonlinearity

In this paper, we consider the following new nonlocal problem: $$\left \{ \textstyle\begin{array}{l@{\quad}l} - (a-b\int_{\varOmega} \vert \nabla u \vert ^{2}\,dx )\Delta u=\lambda f(x) \vert u \vert ^{p-2}u, & x\in\varOmega,\\u=0, & x\in\partial\varOmega, \end{array}\displaystyle \right . $$ where Ω is a smooth bounded domain in $\mathbb{R}^{3}$, $a,b>0$ are constants, $3 0$. Under some assumptions on the sign-changing function f, we obtain the existence of positive solutions via variational methods.