Weakly and strongly singular solutions of semilinear fractional elliptic equations

被引:16
作者
Chen, Huyuan [1 ,2 ]
Veron, Laurent [3 ]
机构
[1] Jiangxi Normal Univ, Dept Math, Nanchang, Peoples R China
[2] Univ Chile, Dept Ingn Matemat, Santiago, Chile
[3] Univ Tours, Lab Math & Phys Theor, Tours, France
关键词
fractional Laplacian; Dirac mass; isolated singularity; weak solution; weakly singular solution; strongly singular solution; REGULARITY;
D O I
10.3233/ASY-141216
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Let Omega subset of R-N (N >= 2) be a bounded C-2 domain containing 0, 0 < alpha < 1 and 0 < p < N/N-2 alpha. If delta(0) is the Dirac mass at 0 and k > 0, we prove that the weakly singular solution u(k) of (E-k) (-Delta)(alpha)u + u(p) - k delta(0) in Omega, which vanishes in Omega(c), is a classical solution of (E-*) (-Delta)(alpha)u + u(p) = 0 in Omega\{0} with the same outer data. Let A = [N/2 alpha, 1 + 2 alpha/N) for N = 2, 3 and root 5-1/4N < alpha < 1, otherwise, A = phi; we derive that u(k) converges to infinity in whole Omega as k -> infinity for p is an element of (0, 1 + 2 alpha/N)\A, while the limit of u(k) is a strongly singular solution of (E-*) for 1 + 2 alpha/N < p < N/N-2 alpha.
引用
收藏
页码:165 / 184
页数:20
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