Multiplicity of positive solution for an indefinite elliptic equation on R-2 with exponential nonlinearities

作者：Mei Linfeng^*

来源：Journal of Mathematical Analysis and Applications, 2008, 341(2): 1334-1353.

DOI：10.1016/j.jmaa.2007.11.023

• indefinite elliptic equation
• exponential nonlinearity
• multiplicity results
• a priori bounds

In this paper, we consider the multiplicity of positive solution to the equation
-Delta u = lambda u + h(x)u(p)e(u), x epsilon R-2,
with h(x) a sign-changing function, p > 1 a constant and lambda 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.

• 出版日期2008-5-15
• 单位山东建筑大学