On the existence of solutions of a $k$-Hessian equation and its connection with self-similar solutions
Year: 2024
Type: article
Abstract: Let $ \alpha,\beta $ be real parameters and let $ a>0 $. We study radially symmetric solutions of$ \begin{equation*} S_k(D^2v)+\alpha v+\beta\xi\cdot\nabla v = 0,\, v>0\;\; \mbox{in}\;\; \mathbb{R}^n,\; v(0) = a, \end{equation*} $where the dot means the usual scalar product in $ \mathbb{R}^n $ and $ S_k(D^2v) $ denotes the $ k $-Hessian operator of $ v $. For $ \beta>0 $ and $ \alpha\leq\frac{\beta(n-2k)}{k}\;\;\mbox{with}\;\;k
DOI: 10.3934/dcds.2024116
Author: Justino Sánchez
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4402208039