Year: 2023
Author: Limin Zhang, Fangfang Liao, Xianhua Tang, Dongdong Qin
Journal of Nonlinear Modeling and Analysis, Vol. 5 (2023), Iss. 2 : pp. 247–271
Abstract
In this paper, we are dedicated to studying the following singularly Choquard equation $$−ε^2∆u + V (x)u = ε^{−α} [I_α ∗ F(u)] f(u), \ x ∈ \mathbb{R}^ 2,$$ where $V (x)$ is a continuous real function on $\mathbb{R}^2,$ $I_α : \mathbb{R}^2 → \mathbb{R}$ is the Riesz potential, and $F$ is the primitive function of nonlinearity $f$ which has critical exponential growth. Using the Trudinger-Moser inequality and some delicate estimates, we show that the above problem admits at least one semiclassical ground state solution, for $ε > 0$ small provided that $V (x)$ is periodic in $x$ or asymptotically linear as $|x| → ∞.$ In particular, a precise and fine lower bound of $\frac{f(t)}{e^{\beta_0 t^2}}$ near infinity is introduced in this paper.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2023.247
Journal of Nonlinear Modeling and Analysis, Vol. 5 (2023), Iss. 2 : pp. 247–271
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Choquard equation critical exponential growth Trudinger-Moser inequality ground state solution.