Multiplicity of positive solution for an indefinite elliptic equation on R2 with exponential nonlinearities

In this paper, we consider the multiplicity of positive solution to the equation − u = λu +h(x)upeu, x∈ R2, with h(x) a sign-changing function, p > 1 a constant and λ a parameter. We first use a moving plane argument to get a priori bounds for the positive solutions of this equation. Then we obtain multiple positive solutions through a squeezing method, which overcomes the lack of compactness of the problem. © 2007 Elsevier Inc. All rights reserved