Separable solutions of quasilinear Lane-Emden equations
نویسندگان
چکیده
For 0 < p − 1 < q and either ǫ = 1 or ǫ = −1, we prove the existence of solutions of −∆pu = ǫu q in a cone CS , with vertex 0 and opening S, vanishing on ∂CS , under the form u(x) = |x|ω( 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. 2010 Mathematics Subject Classification. 35J92, 35J60, 47H11, 58C30.
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