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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2019, Volume 163, Pages 108–112
(Mi into455)
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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.
Citation:
E. E. Kholodnov, “On ground states and compactly supported solutions of elliptic equations with non-Lipschitz nonlinearities”, Differential Equations, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 163, VINITI, Moscow, 2019, 108–112
Linking options:
https://www.mathnet.ru/eng/into455 https://www.mathnet.ru/eng/into/v163/p108
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Abstract page: | 80 | Full-text PDF : | 36 | References: | 21 | First page: | 1 |
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