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

Pages: 445 - 456, Volume 7, Issue 2, March 2008

doi:10.3934/cpaa.2008.7.445       Abstract        Full Text (181.5K)       Related Articles

Cristina Tarsi - Department of Mathematics, Università degli Studi di Milano, Via Saldini 50, Milano, 20133, Italy (email)

Abstract: 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:  Perturbation from symmetry, min-max method, variational methods, Trudinger-Moser inequality, exponential growth.
Mathematics Subject Classification:  Primary: 35J60; Secondary: 58E05.

Received: May 2006;      Revised: May 2007;      Published: December 2007.