Analysis of positive radial solutions for singular superlinear p-Laplacian systems on the exterior of a ball

In this paper, we study some well-posedness properties of a positive radial solution pair (u(1), u(2)) to a singular boundary value problem in the form: {-Delta(p)u(i) - lambda K-i(vertical bar x vertical bar)f(i)(u(j)) in R-N \ B-r0, a(i)partial derivative u(i)/partial derivative n + (c) over tilde (i)(lambda, u(j), u(i))u(i) = 0 on partial derivative B-r0, u(i) -> 0 as vertical bar x vertical bar -> infinity, where i, j is an element of {1, 2}, i not equal j, Delta p stands for the singular\degenerate p-Laplacian Delta(p)w := div(|del w vertical bar(p-2)del w) with 1 < p < N, lambda > 0, a(i) >= 0, r(0) > 0, K-i is an element of C ((r(0), infinity), (0,infinity)), and (c) over tilde (i) is an element of C ((0,infinity) x [0,infinity) x [0,infinity), (0,infinity)). Here the functions f(i) is an element of C ((0,infinity), R), i = 1, 2 satisfy a combined p-superlinear growth at infinity and possibly have singularities at 0. We establish an existence result for the case lambda approximate to 0, multiplicity results of positive radial solutions for certain ranges of lambda, and nonexistence results of a positive radial solution for the case lambda >> 1. (C) 2019 Elsevier Ltd. All rights reserved.