Self-generated interior blow-up solutions in fractional elliptic equation with absorption

Abstract

In this paper, we study positive solutions to problems involving the fractional Laplacian

{(-Delta)(alpha)u(x) + vertical bar u vertical bar(p-1)u(x) = 0, x is an element of Omega \ C,

u(x) = 0, x is an element of Omega(c),

lim(x is an element of Omega\C, x -> C) u(x) = +infinity,

where p > 1 and Omega is an open bounded C-2 domain in R-N, C subset of Omega is a compact C-2 manifold with N - 1 multiples dimensions and without boundary, the operator (-Delta)(alpha) with alpha is an element of (0,1) is the fractional Laplacian. We consider the existence of positive solutions for problem (0.1). Moreover, we further analyze uniqueness, asymptotic behavior and nonexistence.