Weak solutions of semilinear elliptic equation involving Dirac mass
Annales de l'I.H.P. Analyse non linéaire, Volume 35 (2018) no. 3, pp. 729-750.

In this paper, we study the elliptic problem with Dirac mass

{Δu=Vup+kδ0inRN,lim|x|+u(x)=0,
where N>2, p>0, k>0, δ0 is the Dirac mass at the origin and the potential V is locally Lipchitz continuous in RN{0}, with non-empty support and satisfying
0V(x)σ1|x|a0(1+|x|aa0),
with a0<N, a0<a and σ1>0. We obtain two positive solutions of (1) with additional conditions for parameters on a,a0, p and k. The first solution is a minimal positive solution and the second solution is constructed via Mountain Pass Theorem.

DOI: 10.1016/j.anihpc.2017.08.001
Classification: 35J60, 35J20
Keywords: Weak solution, Mountain Pass theorem, Dirac mass
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     title = {Weak solutions of semilinear elliptic equation involving {Dirac} mass},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {729--750},
     publisher = {Elsevier},
     volume = {35},
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Chen, Huyuan; Felmer, Patricio; Yang, Jianfu. Weak solutions of semilinear elliptic equation involving Dirac mass. Annales de l'I.H.P. Analyse non linéaire, Volume 35 (2018) no. 3, pp. 729-750. doi : 10.1016/j.anihpc.2017.08.001. http://archive.numdam.org/articles/10.1016/j.anihpc.2017.08.001/

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