Multiplicity of solutions for a nonlocal nonhomogeneous elliptic equation with critical exponential growth

Abstract

In this paper we are interested in the following nonlocal nonhomogeneous elliptic equation in R2,−Δu+V(x)u=(1|x|μ⁎F(u)|x|β)f(u)|x|β+εh(x)inR2, where V is a positive continuous potential, 0<μ<2, β≥0, 2β+μ≤2, ε 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.