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Separable solutions of quasilinear Lane-Emden equations
- Publication Year :
- 2011
-
Abstract
- 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.<br />Comment: To appear in Journal of the European Mathematical Society
- Subjects :
- Mathematics - Analysis of PDEs
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1104.0479
- Document Type :
- Working Paper