Local solutions for elliptic problems with exponential nonlinearities via finite dimensional reduction Massimo GrossiS. Prashanth 35J60exponential nonlinearityfinite dimensional reductionNirenberg's problem 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. Indiana University Mathematics Journal 2005 text pdf 10.1512/iumj.2005.54.2517 10.1512/iumj.2005.54.2517 en Indiana Univ. Math. J. 54 (2005) 383 - 417 state-of-the-art mathematics http://iumj.org/access/