LAUSR

Abstract In this paper we are interested in the following nonlocal nonhomogeneous elliptic equation in R 2 , − Δ u + V ( x ) u = ( 1 | x | μ ⁎ F ( u ) | x | β ) f ( u ) | x | β + e h ( x ) in R 2 , where V is a positive continuous potential, 0 μ 2 , β ≥ 0 , 2 β + μ ≤ 2 , e is a small parameter and F ( s ) is the primitive function of f ( s ) . Suppose that the nonlinearity f ( s ) is of critical exponential growth in the sense of Trudinger-Moser inequality, we prove the existence and multiplicity of solutions by variational methods.