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We verify the existence of radial positive solutions for the semi-linear equation −∆u = up − V(y)uq, u >0, in RN where N ≥ 3, p is close to p∗ := (N + 2)/(N−2), and V is a radial smooth potential. If q is super-critical, namely q > p∗, we prove that this Problem has a radial solution behaving like a super-position of bubbles blowing-up at the origin with diﬀerent rates of concentration, provided V(0) < 0. On the other hand, if N/(N −2) < q < p∗, we prove that this Problem has a radial solution behaving like a super-position of ﬂat bubbles with diﬀerent rates of concentration, provided limr→∞V(r) < 0.
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- 1 Active
27/04/20 → 26/04/23
Project: Research council