# Stable solutions of $-\Delta u=f\left(u\right)$ in ${\mathbb{R}}^{N}$

Louis Dupaigne; Alberto Farina

Journal of the European Mathematical Society (2010)

- Volume: 012, Issue: 4, page 855-882
- ISSN: 1435-9855

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topDupaigne, Louis, and Farina, Alberto. "Stable solutions of $−\Delta u= f(u)$ in $\mathbb {R}^N$." Journal of the European Mathematical Society 012.4 (2010): 855-882. <http://eudml.org/doc/277779>.

@article{Dupaigne2010,

abstract = {Several Liouville-type theorems are presented for stable solutions of the equation $-\Delta u=f(u)$ in $\mathbb \{R\}^N$, where $f>0$ is a general convex, nondecreasing function. Extensions to solutions which are merely stable outside a compact set are discussed.},

author = {Dupaigne, Louis, Farina, Alberto},

journal = {Journal of the European Mathematical Society},

keywords = {Liouville-type theorems; stable solutions},

language = {eng},

number = {4},

pages = {855-882},

publisher = {European Mathematical Society Publishing House},

title = {Stable solutions of $−\Delta u= f(u)$ in $\mathbb \{R\}^N$},

url = {http://eudml.org/doc/277779},

volume = {012},

year = {2010},

}

TY - JOUR

AU - Dupaigne, Louis

AU - Farina, Alberto

TI - Stable solutions of $−\Delta u= f(u)$ in $\mathbb {R}^N$

JO - Journal of the European Mathematical Society

PY - 2010

PB - European Mathematical Society Publishing House

VL - 012

IS - 4

SP - 855

EP - 882

AB - Several Liouville-type theorems are presented for stable solutions of the equation $-\Delta u=f(u)$ in $\mathbb {R}^N$, where $f>0$ is a general convex, nondecreasing function. Extensions to solutions which are merely stable outside a compact set are discussed.

LA - eng

KW - Liouville-type theorems; stable solutions

UR - http://eudml.org/doc/277779

ER -

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