Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 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
References:
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.
Bibliographic databases:
Document Type: Article
UDC: 517.957
Language: Russian
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
Citation in format AMSBIB
\Bibitem{Kho19}
\by E.~E.~Kholodnov
\paper On ground states and compactly supported solutions of elliptic equations with non-Lipschitz nonlinearities
\inbook Differential Equations
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2019
\vol 163
\pages 108--112
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into455}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4014979}
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    Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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