In this paper we study a nonlocal singularly perturbed Choquard type equation

$$-{\epsilon}^{2}\Delta u+V\left(x\right)u{=}^{\mu -2}\left[\frac{1}{{\left|x\right|}^{\mu}}*\left(P\left(x\right)G\left(u\right)\right)\right]P\left(x\right)g\left(u\right)$$ |

Accepted:

DOI: 10.1051/cocv/2017007

Keywords: Choquard equation, semiclassical solutions, Trudinger-Moser inequality, critical exponential growth

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@article{COCV_2018__24_1_177_0, author = {Yang, Minbo}, title = {Semiclassical ground state solutions for a {Choquard} type equation in $\mathbb{R}^{2}$ with critical exponential growth}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {177--209}, publisher = {EDP-Sciences}, volume = {24}, number = {1}, year = {2018}, doi = {10.1051/cocv/2017007}, mrnumber = {3764139}, zbl = {1400.35086}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2017007/} }

TY - JOUR AU - Yang, Minbo TI - Semiclassical ground state solutions for a Choquard type equation in $\mathbb{R}^{2}$ with critical exponential growth JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2018 SP - 177 EP - 209 VL - 24 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2017007/ DO - 10.1051/cocv/2017007 LA - en ID - COCV_2018__24_1_177_0 ER -

%0 Journal Article %A Yang, Minbo %T Semiclassical ground state solutions for a Choquard type equation in $\mathbb{R}^{2}$ with critical exponential growth %J ESAIM: Control, Optimisation and Calculus of Variations %D 2018 %P 177-209 %V 24 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2017007/ %R 10.1051/cocv/2017007 %G en %F COCV_2018__24_1_177_0

Yang, Minbo. Semiclassical ground state solutions for a Choquard type equation in $\mathbb{R}^{2}$ with critical exponential growth. ESAIM: Control, Optimisation and Calculus of Variations, Volume 24 (2018) no. 1, pp. 177-209. doi : 10.1051/cocv/2017007. http://archive.numdam.org/articles/10.1051/cocv/2017007/

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