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Abstract
We verify the existence of radial positive solutions for the semilinear equation −∆u = u^{p} − V(y)u^{q}, u >0, in R^{N }where N ≥ 3, p is close to p^{∗} := (N + 2)/(N−2), and V is a radial smooth potential. If q is supercritical, namely q > p^{∗,} we prove that this Problem has a radial solution behaving like a superposition of bubbles blowingup 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 superposition of ﬂat bubbles with diﬀerent rates of concentration, provided lim_{r→∞}V(r) < 0.
Original language  English 

Pages (fromto)  283298 
Journal  Journal d'Analyse Mathematique 
Volume  140 
Issue number  1 
DOIs  
Publication status  Published  1 Mar 2020 
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Projects
 1 Active

Concentration phenomena in nonlinear analysis
Engineering and Physical Sciences Research Council
27/04/20 → 26/04/23
Project: Research council