LIMITING BEHAVIOR OF SOLUTIONS TO AN EQUATION WITH THE FRACTIONAL LAPLACIAN

摘要

In this paper, we investigate the limiting behavior of solutions up of the following subcritical problem(-?) α/2 u=|x|~βu~(p-1), u>0, x ? ?; u=0, x ? ?? (0.1) as p tending to the critical exponent 2_α~*, where is the unit ball in R~n centered at the origin, and β > 0, 0 <α < 2; 2 < p < 2_α~* = 2N/N-α.. We show that up concentrates on a point on the boundary of the domain as p→2_α~*.