This paper considers the existence of multiple normalized solutions of the following Schrödinger-Choquard equation \(\begin{cases}- \Delta u = \lambda u + k(\varepsilon x)\,(I_{\alpha} * |u|^{q})\,|u|^{q-2}u + \mu (I_{\alpha} * |u|^{p})\,|u|^{p-2}u, \quad x \in \mathbb{R}^N, \\ \displaystyle \int_{\mathbb{R}^N} |u|^2 \, dx = c^2, \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad x \in \mathbb{R}^N.\end{cases}\) where c, ε, μ > 0, N ≥ 3, α, ∈ (0; N), \({{N + \alpha} \over N} < q < 1 + {{\alpha + 2} \over N} < p \le {{N + \alpha } \over {N - 2}}\) , λ ∈ ℝ is a Lagrange multiplier which is unknown, Iα is the Riesz potential, k:ℝN → [0; ∞) is a continuous and positive function. When ε is small enough, we prove that the numbers of normalized solutions are at least the numbers of global maximum points of k by Ekeland’s variational principle and truncated skill.
