Monotonic convergence of positive radial solutions for general quasilinear elliptic systems

We study the asymptotic behavior of positive radial solutions for quasilinear elliptic systems that have the form { Delta(p)u = c(1)|x|(m)(1 )& sdot; g(1 )(v) & sdot; | del u|(alpha )in R-n, { Delta(p)v = c(2)|x|(m)(2 )& sdot; g(2) (v) & sdot;g(3) (| del u| in R-n, where Delta(p) denotes the p-Laplace operator, p > 1, n >= 2 , c(1), c(2 )> 0 and m(1), m(2), alpha >= 0 . For a general class of functions g(j) which grow polynomially, we show that every non-constant positive radial solution (u, v) asymptotically approaches (u(0), v(0)) = (C-lambda|x|(lambda), C-mu|x|(mu)) for some parameters lambda,mu,C-lambda,C-mu > 0 . In fact, the convergence is monotonic in the sense that both u/u(0) and v/v(0 )are decreasing. We also obtain similar results for more general systems.