Positive radial solutions for p-Laplacian systems

The paper deals with the existence of positive radial solutions for the p-Laplacian system div(vertical bar del u(i)vertical bar(p-2)del u(i)) + f(i)(u(1,)..., u(n)) = 0, vertical bar x vertical bar 1, x epsilon R-N. Here f(i), i = 1,... , n, are continuous and nonnegative functions. Let u = (u(1,)... , u(n)), parallel to u parallel to = Sigma(n)(i=1) vertical bar u(i)vertical bar, f(0)(i) = lim(parallel to u parallel to) - 0 f(i)(u) parallel to u parallel to(p-1), f(infinity)(i) = lim(parallel to u parallel to) - infinity f(i)(u) parallel to u parallel to(p-1), i = 1,..., n, f = (f(1),..., f(n)), f(0) = Sigma(n)(i=1) f(0)(i) and f(infinity)(i). We prove that f(0) = infinity and f(infinity) = 0 (sublinear), guarantee the existence of positive radial solutions for the problem. Our methods employ fixed point theorems in a cone.