|Publication ahead of print|
|Published online||17 January 2018|
Semiclassical ground state solutions for a Choquard type equation in ℝ2 with critical exponential growth∗
Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang, 321004, P.R. China.
Received: 28 September 2016
Accepted: 25 January 2017
In this paper we study a nonlocal singularly perturbed Choquard type equation
in ℝ2, where ε is a positive parameter, with 0 < μ < 2 is the Riesz potential, ∗ is the convolution operator, V(x), P(x) are two continuous real functions and G(s) is the primitive function of g(s). Suppose that the nonlinearity g is of critical exponential growth in ℝ2 in the sense of the Trudinger-Moser inequality, we establish some existence and concentration results of the semiclassical solutions of the Choquard type equation in the whole plane. As a particular case, the concentration appears at the maximum point set of P(x) if V(x) is a constant.
Mathematics Subject Classification: 35J25 / 35J20 / 35J60
Key words: Choquard equation / semiclassical solutions / Trudinger-Moser inequality / critical exponential growth
© EDP Sciences, SMAI 2018
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