Sign-changing blow-up solutions for Hénon type elliptic equations with exponential nonlinearity
The paper deals with the existence of sign-changing solutions with multiple concentration to the Dirichlet problem \[ \begin{cases} -\Delta u=\varepsilon^2| x|^{2\alpha} (e^u-e^{-u}) & \text{in }\Omega,\\ u=0 & \text{on }\partial\Omega, \end{cases} \] where \(\alpha>0\), \(\Omega\) is a smooth and bounded domain in \(\mathbb R^2\) which contains the origin, and \(\varepsilon>0\) is a small parameter. It is proved that if \(\alpha\neq 1\) then a nodal solution exists with a number of mixed positive and negative blow-up points up to 4.
scientific article; zbMATH DE number 6475676