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.

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - E. E. Kholodnov
TI  - On ground states and compactly supported solutions of elliptic equations with non-Lipschitz nonlinearities
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2019
SP  - 108
EP  - 112
VL  - 163
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2019_163_a7/
LA  - ru
ID  - INTO_2019_163_a7
ER  - 
%0 Journal Article
%A E. E. Kholodnov
%T On ground states and compactly supported solutions of elliptic equations with non-Lipschitz nonlinearities
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2019
%P 108-112
%V 163
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2019_163_a7/
%G ru
%F INTO_2019_163_a7
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/

[1] Ilyasov Ya. Sh., Kholodnov E. E., “O globalnoi neustoichivosti reshenii giperbolicheskikh uravnenii s nelipshitsevoi nelineinostyu”, Ufim. mat. zh., 9:4 (2017), 45–54

[2] Díaz J. I., Hernández J., Il'yasov Y., “Flat solutions of some non-Lipschitz autonomous semilinear equations may be stable for $N\ge3$”, Chin. Ann. Math. Ser. B., 38:1 (2017), 345–378 | DOI | MR | Zbl

[3] Díaz J. I., Hernández J., Il'yasov Y., “On the existence of positive solutions and solutions with compact support for a spectral nonlinear elliptic problem with strong absorption”, Nonlin. Anal. Theory Meth. Appl., 119 (2015), 484–500 | DOI | MR | Zbl

[4] Il'yasov Y. S., “On critical exponent for an elliptic equation with non-Lipschitz nonlinearity”, Dynam. Syst., 2011, 698–706 | MR | Zbl

[5] Il'yasov Y. S., Egorov Y., “Höpf maximum principle violation for elliptic equations with non-Lipschitz nonlinearity”, Nonlin. Anal., 72 (2010), 3346–3355 | DOI | MR | Zbl

[6] Kaper H. G., Kwong M. K., “Free boundary problems for Emden–Fowler equations”, Differ. Integr. Equations., 3:2 (1990), 353–362 | MR | Zbl

[7] Kaper H., Kwong M. K., Li Y., “Symmetry results for reaction-diffusion equations”, Differ. Integr. Equations., 6 (1993), 1045–1056 | MR | Zbl

[8] Serrin J., Zou H., “Symmetry of ground states of quasilinear elliptic equations”, Arch. Rat. Mech. Anal., 148:4 (1999), 265–290 | DOI | MR | Zbl