Separable solutions of quasilinear Lane-Emden equations

For 0 < p - 1 < q and either epsilon = 1 or epsilon = -1, we prove the existence of solutions of -Delta(p)u = epsilon u(q) in a cone C-S, with vertex 0 and opening S, vanishing on partial derivative C-S, of the form u(x) = vertical bar x vertical bar(-beta) omega(x/vertical bar x vertical bar). The problem reduces to a quasilinear elliptic equation on S and the existence proof is based upon degree theory and homotopy methods. We also obtain a nonexistence result in some critical case by making use of an integral type identity.