Large solutions to elliptic equations involving fractional Laplacian
Annales de l'I.H.P. Analyse non linéaire, Volume 32 (2015) no. 6, p. 1199-1228
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The purpose of this paper is to study boundary blow up solutions for semi-linear fractional elliptic equations of the form {(-Δ) α u(x)+|u| p-1 u(x)=f(x),xΩ,u(x)=0,xΩ ¯ c , lim xΩ,xΩu(x)=+,(0.1) where p>1, Ω is an open bounded C 2 domain of N , N2, the operator (-Δ) α with α(0,1) is the fractional Laplacian and f:Ω is a continuous function which satisfies some appropriate conditions. We obtain that problem (0.1) admits a solution with boundary behavior like d(x) -2α p-1 , when 1+2α<p<1-2α τ 0 (α), for some τ 0 (α)(-1,0), and has infinitely many solutions with boundary behavior like d(x) τ 0 (α) , when max {1-2α τ 0 +τ 0 (α)+1 τ 0 ,1}<p<1-2α τ 0 . Moreover, we also obtained some uniqueness and non-existence results for problem (0.1).

DOI : https://doi.org/10.1016/j.anihpc.2014.08.001
Keywords: Large solutions, Fractional Laplacian, Existence, Uniqueness, Non-existence infinite existence
@article{AIHPC_2015__32_6_1199_0,
     author = {Chen, Huyuan and Felmer, Patricio and Quaas, Alexander},
     title = {Large solutions to elliptic equations involving fractional Laplacian},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {32},
     number = {6},
     year = {2015},
     pages = {1199-1228},
     doi = {10.1016/j.anihpc.2014.08.001},
     zbl = {06520570},
     mrnumber = {3425260},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2015__32_6_1199_0}
}
Chen, Huyuan; Felmer, Patricio; Quaas, Alexander. Large solutions to elliptic equations involving fractional Laplacian. Annales de l'I.H.P. Analyse non linéaire, Volume 32 (2015) no. 6, pp. 1199-1228. doi : 10.1016/j.anihpc.2014.08.001. http://www.numdam.org/item/AIHPC_2015__32_6_1199_0/

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