This paper is devoted to study the slightly subcritical problem with double nonlocal terms \(\begin{aligned} \left\{ \begin{array}{ll} \displaystyle {(-\Delta )^{s}u=\bigg (\int _{\Omega }\frac{u^{2^{*}_{\alpha ,s}-\varepsilon }(y)}{|x-y|^{\alpha }}dy\bigg ) u^{2^{*}_{\alpha ,s}-1-\varepsilon }}, & \text { in } \Omega ,\\ u>0, & \text { in } \Omega ,\\ u=0, & \text { in } {\mathbb {R}}^{N}\setminus \Omega , \end{array}\right. \end{aligned}\) where \(\Omega \subset {\mathbb {R}}^{N}\) (with \(C^2\) boundary regularity) is a smooth bounded domain with \(N>2s\) , \(s\in (0,\min \{1,\frac{3N-2}{6}\})\) , \(\alpha \in (0,\min \{4s,N\})\) , \(2^{*}_{\alpha ,s}=\frac{2N-\alpha }{N-2s}\) is the upper critical exponent in the sense of the Hardy-Littlewood-Sobolev inequality, and \(\varepsilon >0\) is a small parameter. Using the finite-dimensional reduction method, we construct a solution for the above problem which concentrates around the local minimum point of the Robin function as \(\varepsilon \) goes to zero.
