Geodesic
Separable solutions of quasilinear Lane–Emden equations
Journal of the European Mathematical Society, Tome 15 (2013) no. 3, pp. 755-774 Cet article a éte moissonné depuis la source EMS Press

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For 0−1either ε=1 or ε=−1, we prove the existence of solutions of −Δp​u=εuq in a cone CS​, with vertex 0 and opening S, vanishing on ∂CS​, under the form u(x)=∣x∣−βω(∣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.
DOI : 10.4171/jems/375
Classification : 35-XX, 47-XX, 58-XX, 00-XX
Keywords: Quasilinear elliptic equations, p-Laplacian, cones, Leray–Schauder degree 
@article{JEMS_2013_15_3_a2,
     author = {Alessio Porretta and Laurent V\'eron},
     title = {Separable solutions of quasilinear {Lane{\textendash}Emden} equations},
     journal = {Journal of the European Mathematical Society},
     pages = {755--774},
     year = {2013},
     volume = {15},
     number = {3},
     doi = {10.4171/jems/375},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/375/}
}
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Alessio Porretta; Laurent Véron. Separable solutions of quasilinear Lane–Emden equations. Journal of the European Mathematical Society, Tome 15 (2013) no. 3, pp. 755-774. doi: 10.4171/jems/375

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