Least energy solutions for Choquard equations involving vanishing potentials and exponential growth

Least energy solutions for Choquard equations involving vanishing potentials and exponential growth

Článek WoS

In this paper, we consider the existence of solutions for Choquard equation of the form -Delta u+V(|x|)u=[I alpha & lowast;(Q(|x|)F(u))]Q(|x|)f(u),x is an element of R2,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} -\Delta u+V(|x|) u =[I_\alpha *(Q(|x|)F(u))]Q(|x|)f(u), \ \ \ \ x\in \mathbb {R}{2}, \end{aligned}$$\end{document}where the nonlinear term f has exponential growth, the radial potentials V,Q:R+-> R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V,\ Q: \mathbb {R}{+} \rightarrow \mathbb {R}$$\end{document} are unbounded, singular at the origin or decaying to zero. By combining the variational methods, Trudinger-Moser inequality and some new approaches to estimate precisely the minimax level of the energy functional, we prove the existence of a nontrivial solution for the above problem under some weaker assumptions. Our study extends and improves the results of [Albuquerque-Ferreira-Severo, Milan J. Math. 89 (2021)] and [Alves-Shen, J. Differential Equations, 344 (2023)].

In this paper, we consider the existence of solutions for Choquard equation of the form -Delta u+V(|x|)u=[I alpha & lowast;(Q(|x|)F(u))]Q(|x|)f(u),x is an element of R2,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} -\Delta u+V(|x|) u =[I_\alpha *(Q(|x|)F(u))]Q(|x|)f(u), \ \ \ \ x\in \mathbb {R}{2}, \end{aligned}$$\end{document}where the nonlinear term f has exponential growth, the radial potentials V,Q:R+-> R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V,\ Q: \mathbb {R}{+} \rightarrow \mathbb {R}$$\end{document} are unbounded, singular at the origin or decaying to zero. By combining the variational methods, Trudinger-Moser inequality and some new approaches to estimate precisely the minimax level of the energy functional, we prove the existence of a nontrivial solution for the above problem under some weaker assumptions. Our study extends and improves the results of [Albuquerque-Ferreira-Severo, Milan J. Math. 89 (2021)] and [Alves-Shen, J. Differential Equations, 344 (2023)].

Choquard equations; Critical exponential growth; Trudinger-Moser inequality

Choquard equations; Critical exponential growth; Trudinger-Moser inequality

JIN, P.; RADULESCU, V.; TANG, X.; WEN, L.

2026

29.01.2026

Springer Nature

Revista de la Real Academia de Ciencias Exactas Fisicas y Naturales Serie A-Matematicas

120

2

Španělské království

1

30

30

https://link.springer.com/article/10.1007/s13398-025-01825-x

http://hdl.handle.net/11012/256477