主 题: Large solutions to elliptic equations involving fractional Laplacian
报告人: 陈虎元 (New York University Shanghai, China)
时 间: 2014-11-28 10:10-11:10
地 点: 理科一号楼1479（主持人：郭紫华）
In this talk, we will discuss boundary blow up solutions for semilinear fractional elliptic equations
(??)αu(x) +|u|p?1u(x) = 0,
x ∈ ?, u(x) = 0, x ∈ ? ?c,
limx∈?,x→?? u(x) = +∞, (0.1)
where p > 1, ? is an open bounded C2 domain of RN(N ≥ 2) and the operator (??)α with α ∈ (0,1) is the fractional Laplacian. We show that problem (0.1) admits a solution with behavior d(x)? 2α p?1 when 1 + 2α < p < 1 ? 2α τ0(α) for some τ0(α) ∈ (?1,0) and has in?nitely many solutions with behavior d(x)τ0(α) when max{1? 2α τ0(α) + τ0(α)+1 τ0(α) ,1} < p < 1? 2α τ0(α).
References
[1] P. Felmer and A. Quaas, Boundary blow up solutions for fractional el- liptic equations. Asymptotic Analysis, Volume 78 (3), 123-144, 2012.
[2] Y. Du and Q. Huang, Blow-up solutions for a class of semilinear elliptic and parabolic equations, SIAM J. Math. Anal., 31, 1-18, 1999.
[3] H. Chen, P. Felmer and A. Quaas, Large solution to elliptic equation- s involving fractional Laplacian, accepted by Ann. Inst. H. Poincar?e, Analyse Non Lin?eaire, DOI: 10.1016/j.anihpc.2014.08.001.
[4] L. V?eron, Semilinear elliptic equations with uniform blow-up on the boundary, J. Anal. Math., 59(1), 231-250, 1992.
