An elliptic cross-diffusion system describing two-species models on a bounded domain with different natural conditions

This paper is concerned with an elliptic cross-diffusion system describing two species models on a bounded domain Omega, where Omega consists of a finite number of subdomains Omega(i) (i = 1, ..., m) separated by interfaces Gamma(j) (j = 1, ..., m - 1) and the natural conditions of the subdomains Omega(i) are different. This system is strongly coupled and the coefficients of the equations are allowed to be discontinuous on interfaces Gamma(j). The main goal is to show the existence of nonnegative solutions for the system by Schauder's fixed point theorem. Furthermore, as applications, the existence of positive solutions for some Lotka-Volterra models with cross-diffusion, self-diffusion and discontinuous coefficients are also investigated. (C) 2016 Elsevier Inc. All rights reserved.