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27) hold. 12) with κ(q − m) in place of κ (note that q = m∗ > m). 3. The case m∗ < q < m∗ . 10). 1 Note that κq < − m . 1 Let κ be an arbitrary real number; we will treat the two cases κ < − m and κ > κq separately. 12). 12) follows again. 9. 1). 1). 1) we have u(0) = δ p−q β and the first part of Theorem 6 follows. Since v = v(r) solves the ordinary differential equation rn−1 v (r) m−1 = rn−1 (−v q−1 (r) + v p−1 (r)), after integration over [0, r] we obtain v (r) m−1 = r 1 rn−1 tn−1 (−v q−1 (t) + v p−1 (t)) dt = 0 r 1 rn−1 tn−1 (−β q−1 + β p−1 + o(1)) dt 0 r = (−β q−1 + β p−1 + o(1)) as r → 0.

Eq. C. A. Peletier, Quasilinear elliptic equations with nearly critical growth, Comm. Part. Diff. Eq. 14, 1989, 1351-1383 E. Mitidieri, S. Pohoˇzaev, Apriori estimates and blow-up of solutions to nonlinear partial differential equations and inequalities, Proc. Steklov Inst. Math. M. Ni, J. Serrin, Non existence theorems for quasilinear partial differential equations, Rend. Circolo Mat. M. Ni, J. Serrin, Existence and non existence theorems for ground states of quasilinear partial differential equations.

J. 49, 2000, 897-923 J. Serrin, H. Zou, Cauchy-Liouville and universal boundedness theorems for quasilinear elliptic equations and inequalities, to appear in Acta Math. G. Talenti, Best constant in Sobolev inequality, Ann. Mat. Pura Appl. L. V´ azquez, L. Veron, Removable singularities of some strongly nonlinear elliptic equations, Manuscripta Math.

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