IUMJ

Title: Local solutions for elliptic problems with exponential nonlinearities via finite dimensional reduction

Authors: Massimo Grossi and S. Prashanth

Issue: Volume 54 (2005), Issue 2, 383-417

Abstract:

In this paper we prove some existence and multiplicity results for solutions of the problem \[ -\Delta u=e^u+\ve f(x,u)\quad\mbox{in }\mathbb{R}^2. \] These results are related to Nirenberg's problem and the existence of standing wave solutions for the nonlinear Schr\"odinger equation.