Geodesic
On ground states and compactly supported solutions of elliptic equations with non-Lipschitz nonlinearities
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations, Tome 163 (2019), pp. 108-112

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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\alpha1. \end{equation*} The problem of the existence of a solution of the ground-state-type with compact support is examined.
Mots-clés : elliptic equation
Keywords: solution with compact support, non-Lipschitz nonlinearity. 
@article{INTO_2019_163_a7,
     author = {E. E. Kholodnov},
     title = {On ground states and compactly supported solutions of elliptic equations with {non-Lipschitz} nonlinearities},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {108--112},
     publisher = {mathdoc},
     volume = {163},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2019_163_a7/}
}
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E. E. Kholodnov. On ground states and compactly supported solutions of elliptic equations with non-Lipschitz nonlinearities. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations, Tome 163 (2019), pp. 108-112. http://geodesic.mathdoc.fr/item/INTO_2019_163_a7/