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Additional info for Asymptotic behavior of ground states of quasilinear elliptic problems with two vanishing parameters, Part III
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.
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