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Finding invariant tori with Poincare's map
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 |
$ -\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 $f(u)$.
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