For $0 < p-1 < q$ and $\ge=\pm 1$, we prove the existence of solutions of
$-\Gd_pu=\ge u^q$ in a cone $C_S$, with vertex 0 and opening $S$, vanishing on
$\prt C_S$, under the form $u(x)=|x|^\gb\gw(\frac{x}{|x|})$. The problem
reduces to a quasilinear elliptic equation on $S$ and existence is based upon
degree theory and homotopy methods. We also obtain a non-existence result in
some critical case by an integral type identity.Comment: To appear in Journal of the European Mathematical Societ

Alessio Porretta

Laurent Véron

Tor Vergata

Università Roma

Université François Rabelais

English

arXiv

J. Eur. Math. Soc. 15, 755-774 (2013)For $0 < p-1 < q$ and $\ge=\pm 1$, we prove the existence of solutions of $-\Gd_pu=\ge u^q$ in a cone $C_S$, with vertex $0$ and opening $S$, vanishing on $\prt C_S$, under the form $u(x)=|x|^\gb\gw(\frac{x}{|x|})$. The problem reduces to a quasilinear elliptic equation on $S$ and existence is based upon degree theory and homotopy methods. We also obtain a non-existence result in some critical case by an integral type identity

Separable solutions of quasilinear Lane-Emden equations

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