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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 $\mathbb{R} ^2$

Cristina Tarsi 1,

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 $f(u)$.

Keywords: exponential growth., Trudinger-Moser inequality, min-max method, variational methods, Perturbation from symmetry.
Mathematics Subject Classification: Primary: 35J60; Secondary: 58E0.
Citation: Cristina Tarsi. Perturbation from symmetry and multiplicity of solutions for elliptic problems with subcritical exponential growth in $\mathbb{R} ^2$. Communications on Pure and Applied Analysis, 2008, 7 (2) : 445-456. doi: 10.3934/cpaa.2008.7.445
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