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JOURNALS // Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory // Archive

Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 2019 Volume 163, Pages 108–112 (Mi into455)

On ground states and compactly supported solutions of elliptic equations with non-Lipschitz nonlinearities

E. E. Kholodnov

Institution of Russian Academy of Sciences Institute of Mathematics with Computer Center, Ufa

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.

UDC: 517.957

MSC: 35B44, 35B32, 35K59, 35J60, 35J70



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