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Abstract
We verify the existence of radial positive solutions for the semilinear equation (Formula presented.) 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 
Number of pages  16 
Journal  Journal d'Analyse Mathematique 
Volume  140 
Issue number  1 
DOIs  
Publication status  Published  1 Mar 2020 
Bibliographical note
Funding Information:The first author is supported by FONDECYT Grant 1160135 and Millennium Nucleus Center for Analysis of PDE, NC130017. The second author was supported by FAPESP (Brazil) Grant #2016/049257.
Publisher Copyright:
© 2020, The Hebrew University of Jerusalem.
ASJC Scopus subject areas
 Analysis
 Mathematics(all)
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Concentration phenomena in nonlinear analysis
Engineering and Physical Sciences Research Council
27/04/20 → 31/07/24
Project: Research council