For and either or , we prove the existence of solutions of in a cone , with vertex and opening , vanishing on , under the form . The problem reduces to a quasilinear elliptic equation on 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.
Cite this article
Laurent Véron, Alessio Porretta, Separable solutions of quasilinear Lane–Emden equations. J. Eur. Math. Soc. 15 (2013), no. 3, pp. 755–774DOI 10.4171/JEMS/375