Positive radial solutions to classes of p-Laplacian systems on the exterior of a ball with nonlinear boundary conditions

An n x n degenerate elliptic system associated with the p-Laplacian {-Delta(pi) u(i) = lambda K-i(vertical bar x vertical bar)f(i)(u(i+1)) in Omega, kappa(i)partial derivative u(i)/partial derivative n + g(i)(lambda, u(1), u(2), ..., u(n))u(i) = 0 on partial derivative Omega, u(i) -> 0 as vertical bar x vertical bar -> infinity, i = 1, 2, ..., n. is studied in this paper in an exterior domain Omega := { x is an element of R-N vertical bar vertical bar x vertical bar > r(0) > 0}, where 1 < p(i) < N, lambda > 0, kappa(i) >= 0, and the functions K-i > 0, g(i) > 0, and f(i) are continuous. This type of nonlinear problems with a nonlinear boundary condition arise in applications such as chemical kinetics and population distribution. Through a fixed-point theorem of the Krasnoselskii type, we prove, in different situations, the existence, multiplicity, or nonexistence of positive radial solutions according to the distinct behaviors of f(i) near 0 and near infinity. The new traits of the underlying system include relaxation of the restriction n = 2 to any general n >= 2, different p-Laplacian operators for component solutions, the mixed boundary condition, and possible singularities at 0 possessed by and negativity near 0 of the functions f(i). (C) 2021 Elsevier Ltd. All rights reserved.