In this paper, we study the existence of normalized solutions to the following nonlinear Choquard equation with exponential growth \begin{align*} \left\{\begin{aligned}&-\Delta u+\lambda u=(I_{\alpha}\ast F(u))f(u), \quad\quad\hbox{in }\mathbb{R}^{2},\\&\int_{\mathbb{R}^{2}}|u|^{2}dx=a^{2},\end{aligned}\right.\end{align*} where $a>0$ is prescribed, $\lambda\in \mathbb{R}$, $\alpha\in(0,2)$, $I_{\alpha}$ denotes the Riesz potential, $\ast$ indicates the convolution operator, the function $f(t)$ has exponential growth in $\mathbb{R}^{2}$ and $F(t)=\int^{t}_{0}f(\tau)d\tau$. Using the Pohozaev manifold and variational methods, we establish the existence of normalized solutions to the above problem. 2020 Mathematics Subject Classiffication: 35J47; 35B33; 35J50.

In this paper, using the Moser functions and linking theorem, we study the existence of solutions for a class of Hamiltonian Choquard-type elliptic systems in the plane with exponential growth involving singular weights.

In this paper, we study the existence of normalized solutions to the following nonlinear Choquard equation with exponential growthwhere a > 0 is prescribed, λ ∈ R, α ∈ (0, 2), I α denotes the Riesz potential, * indicates the convolution operator, the function f (t) has exponential growth in R 2 and F (t) = ∫ t 0 f (τ )dτ . Using the Pohozaev manifold and variational methods, we establish the existence of normalized solutions to the above problem.