Abstract
We examine the following degenerate elliptic system:
-Delta(s)u =v(p), -Delta(s)v=u(theta), u, v > 0 in R-N = R-N1 xR(N2), where s >= 0 and p, theta> 0. We prove that the system has no stable solution provided p, theta > 0 and N-s := N-1 + (1+ s)N-2 < 2 + alpha + beta, where
alpha = 2(p + 1)/p theta -1 and beta = 2(theta + 1)/p theta -1.
This result is an extension of some results in [15]. In particular, we establish a new integral estimate for u and v (see Proposition 1.1), which is crucial to deal with the case 0 < p < 1.