March  2008, 7(2): 445-456. doi: 10.3934/cpaa.2008.7.445

Perturbation from symmetry and multiplicity of solutions for elliptic problems with subcritical exponential growth in $\mathbb{R} ^2$

1. 

Department of Mathematics, Università degli Studi di Milano, Via Saldini 50, Milano, 20133, Italy

Received  May 2006 Revised  May 2007 Published  December 2007

We consider the following boundary value problem

$ -\Delta u= g(x,u) + f(x,u)\quad x\in \Omega $

$u=0\quad x\in \partial \Omega$

where $g(x,-\xi )=-g(x,\xi)$ and $g$ has subcritical exponential growth in $\mathbb R^2$. Using the method developed by Bolle, we prove that this problem has infinitely many solutions under suitable conditions on the growth of $g(u)$ and $f(u)$.

Citation: Cristina Tarsi. Perturbation from symmetry and multiplicity of solutions for elliptic problems with subcritical exponential growth in $\mathbb{R} ^2$. Communications on Pure & Applied Analysis, 2008, 7 (2) : 445-456. doi: 10.3934/cpaa.2008.7.445
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