| Abstract: |
| We consider low energy nodal radial solutions of Trudinger-Moser critical equations in $\mathbb{R}^2$. We study the asymptotic behavior of them as the growth rate of the nonlinearity goes to a threshold between the existence and nonexistence of nodal radial solutions. The solution exhibits a multiple concentration behavior together with a convergence to the least energy solution of a critical problem. We also observe that each concentration part, with an appropriate scaling, converges to a solution of the classical Liouville problem in $\mathbb{R}^2$. This talk is based on a joint work with Massimo Grossi at Sapienza University of Rome. |
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