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 growth \begin{align*} \left\{ \begin{aligned} &-Δu+λu=(I_α\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 $F(t)={\int }_0^{t}f(\tau )d\tau$. Using the Pohozaev manifold and variational methods, we establish the existence of normalized solutions to the above problem.

arXiv admin note: text overlap with arXiv:2210.02331. text overlap with arXiv:2102.03001 by other authors

References in corpus (1)

• A mass supercritical problem revisited

Cited by in corpus (1)

• Positive solutions with prescribed mass for a planar Choquard equation with critical growth