| Abstract
| - In this paper we study a nonlocal singularly perturbed Choquard type equation. $$-\varepsilon^2\Delta u +V(x)u =\vr^{\mu-2}\left[\frac{1}{|x|^{\mu}}\ast \big(P(x)G(u)\big)\right]P(x)g(u)$$ in ℝ 2, where ε is a positive parameter, \hbox{$\frac{1}{|x|^\mu}$} 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 ℝ 2 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.
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