Existence Results for Fractional Choquard Equations with Critical or Supercritical Growth

Abstract In this paper, we study the following fractional Choquard equation with critical or supercritical growth $$\begin{aligned} \ (-\Delta )^su+V(x)u=f(x,u)+\lambda \left[ |x|^{-\mu }*|u|^p\right] p|u|^{p-2}u, \quad x \in {\mathbb {R}}^N, \end{aligned}$$ ( - Δ ) s u + V x = f , λ | μ ∗ p 2 ∈ R N where $$0<s<1$$ 0 < 1 , $$(-\Delta )^s$$ denotes Laplacian of order s $$N>2s$$ > $$0<\mu <2s$$ and $$p\ge 2_{\mu ,s}^*:=\frac{2N-\mu }{N-2s}$$ ≥ : which is exponent in sense Hardy-Littlewood-Sobolev inequality. Under some suitable conditions, prove that admits a nontrivial solution for small $$\lambda >0$$ by variational methods, extends results Bhattarai J. Differ. Equ. 263 3197–3229 (2017).