LIOUVILLE TYPE THEOREMS FOR STABLE SOLUTIONS OF THE WEIGHTED FRACTIONAL LANE-EMDEN SYSTEM

In this paper, we prove Liouville type theorems for stable solutions to the weighted fractional Lane-Emden system (-delta)(s)u = h(x)vp , (-delta)(s)v = h(x)u(q) , u, v > 0 in R-N , where 1 < q <= p and h is a positive continuous function in R-N satisfying lim inf ( |x|->infinity) h(x)/(x)l > 0 with l > 0. Our results generalize the results established in[23] for the Laplacian case (correspond to s = 1) and improve the previous work [12]. As a consequence, we prove classification result for stable solutions to the weighted fractional Lane-Emden equation (-delta)(s)u = h(x)u(p) in R-N.