# Separable solutions of quasilinear Lane–Emden equations

Alessio Porretta; Laurent Véron

Journal of the European Mathematical Society (2013)

- Volume: 015, Issue: 3, page 755-774
- ISSN: 1435-9855

## Access Full Article

top## Abstract

top## How to cite

topPorretta, Alessio, and Véron, Laurent. "Separable solutions of quasilinear Lane–Emden equations." Journal of the European Mathematical Society 015.3 (2013): 755-774. <http://eudml.org/doc/277354>.

@article{Porretta2013,

abstract = {For $0<p-1<q$ and either $\epsilon =1$ or $\epsilon = -1$, we prove the existence of solutions of $-\Delta _pu=\epsilon u^q$ in a cone $C_S$, with vertex 0 and opening $S$, vanishing on $\partial C_S$, of the form $u(x)=\left|x\right|^\{-\beta \}\omega (x/\left|x\right|)$. The problem reduces to a quasilinear elliptic equation on $S$ and the existence proof is based upon degree theory and homotopy methods. We also obtain a nonexistence result in some critical case by making use of an integral type identity.},

author = {Porretta, Alessio, Véron, Laurent},

journal = {Journal of the European Mathematical Society},

keywords = {quasilinear elliptic equations; $p$-Laplacian; cones; Leray-Schauder degree; quasilinear elliptic equations; -Laplacian; cones; Leray-Schauder degree},

language = {eng},

number = {3},

pages = {755-774},

publisher = {European Mathematical Society Publishing House},

title = {Separable solutions of quasilinear Lane–Emden equations},

url = {http://eudml.org/doc/277354},

volume = {015},

year = {2013},

}

TY - JOUR

AU - Porretta, Alessio

AU - Véron, Laurent

TI - Separable solutions of quasilinear Lane–Emden equations

JO - Journal of the European Mathematical Society

PY - 2013

PB - European Mathematical Society Publishing House

VL - 015

IS - 3

SP - 755

EP - 774

AB - For $0<p-1<q$ and either $\epsilon =1$ or $\epsilon = -1$, we prove the existence of solutions of $-\Delta _pu=\epsilon u^q$ in a cone $C_S$, with vertex 0 and opening $S$, vanishing on $\partial C_S$, of the form $u(x)=\left|x\right|^{-\beta }\omega (x/\left|x\right|)$. The problem reduces to a quasilinear elliptic equation on $S$ and the existence proof is based upon degree theory and homotopy methods. We also obtain a nonexistence result in some critical case by making use of an integral type identity.

LA - eng

KW - quasilinear elliptic equations; $p$-Laplacian; cones; Leray-Schauder degree; quasilinear elliptic equations; -Laplacian; cones; Leray-Schauder degree

UR - http://eudml.org/doc/277354

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.