Abstract:
In a bounded domain $\Omega\subset\mathbb{R}^N$, we consider the Dirichlet boundary-value problem for an elliptic equation with a non-Lipschitz nonlinearity of the form
\begin{equation*}
\Delta u = \lambda u-|u|^{\alpha-1}u,
\quad \lambda \in \mathbb{R}, \quad 0<\alpha<1.
\end{equation*}
The problem of the existence of a solution of the ground-state-type with compact support is examined.
Keywords:elliptic equation, solution with compact support, non-Lipschitz nonlinearity.