@Article{JNMA-5-2,
author = {Zhang, Limin and Liao, Fangfang and Xianhua, Tang and Qin, Dongdong},
title = {Ground States for Singularly Perturbed Planar Choquard Equation with Critical Exponential Growth},
journal = {Journal of Nonlinear Modeling and Analysis},
year = {2023},
volume = {5},
number = {2},
pages = {247--271},
abstract = {<p style="text-align: justify;">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 $ε &gt; 0$ 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.</p>},
issn = {2562-2862},
doi = {https://doi.org/10.12150/jnma.2023.247},
url = {https://global-sci.com/article/87869/ground-states-for-singularly-perturbed-planar-choquard-equation-with-critical-exponential-growth}
}