SEMICLASSICAL GROUND STATE SOLUTIONS FOR A CHOQUARD TYPE EQUATION IN R2 WITH CRITICAL EXPONENTIAL GROWTH.

In this paper we study a nonlocal singularly perturbed Choquard type equation -ε²Δu + V (x)u = ε^µ-2[1/|x|^µ*(P(x)G(u))]P(x)g(u) in R², where e is a positive parameter, 1/|x|^µ 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. [ABSTRACT FROM AUTHOR]