Normalized solutions for a Choquard equation with exponential growth in $$\mathbb {R}^{2}$$

Abstract

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.